[{"abstract":[{"lang":"eng","text":"We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. "}],"doi":"10.4064/aa211207-16-5","title":"The asymptotics of nilpotent Galois groups","external_id":{"arxiv":["2011.04325 "]},"keyword":["Algebra and Number Theory"],"user_id":"93826","type":"journal_article","publication":"Acta Arithmetica","issue":"2","page":"165-184","volume":204,"intvolume":" 204","author":[{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"department":[{"_id":"102"}],"citation":{"mla":"Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta Arithmetica, vol. 204, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2022, pp. 165–84, doi:10.4064/aa211207-16-5.","bibtex":"@article{Klüners_2022, title={The asymptotics of nilpotent Galois groups}, volume={204}, DOI={10.4064/aa211207-16-5}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2022}, pages={165–184} }","short":"J. Klüners, Acta Arithmetica 204 (2022) 165–184.","apa":"Klüners, J. (2022). The asymptotics of nilpotent Galois groups. Acta Arithmetica, 204(2), 165–184. https://doi.org/10.4064/aa211207-16-5","ama":"Klüners J. The asymptotics of nilpotent Galois groups. Acta Arithmetica. 2022;204(2):165-184. doi:10.4064/aa211207-16-5","chicago":"Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta Arithmetica 204, no. 2 (2022): 165–84. https://doi.org/10.4064/aa211207-16-5.","ieee":"J. Klüners, “The asymptotics of nilpotent Galois groups,” Acta Arithmetica, vol. 204, no. 2, pp. 165–184, 2022, doi: 10.4064/aa211207-16-5."},"publication_status":"published","language":[{"iso":"eng"}],"year":"2022","publication_identifier":{"issn":["0065-1036","1730-6264"]},"status":"public","date_created":"2022-12-22T10:08:23Z","publisher":"Institute of Mathematics, Polish Academy of Sciences","date_updated":"2023-03-06T08:48:33Z","_id":"34835"},{"keyword":["Algebra and Number Theory"],"user_id":"81636","doi":"10.1112/s0010437x20007551","abstract":[{"lang":"eng","text":"The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\\Pi$ of $\\operatorname {GL}_{2n}$ over a totally real field $F$ admitting a Shalika model. We use a modular symbol approach, along the global lines of the work of Ash and Ginzburg, but our results are more definitive because we draw heavily upon the methods used in the recent and separate works of all three authors. By construction, our $p$-adic $L$-functions are distributions on the Galois group of the maximal abelian extension of $F$ unramified outside $p\\infty$. Moreover, we work under a weaker Panchishkine-type condition on $\\Pi _p$ rather than the full ordinariness condition. Finally, we prove the so-called Manin relations between the $p$-adic $L$-functions at all critical points. This has the striking consequence that, given a unitary $\\Pi$ whose standard $L$-function admits at least two critical points, and given a prime $p$ such that $\\Pi _p$ is ordinary, the central critical value $L(\\frac {1}{2}, \\Pi \\otimes \\chi )$ is non-zero for all except finitely many Dirichlet characters $\\chi$ of $p$-power conductor."}],"title":"L-functions of GL(2n): p-adic properties and non-vanishing of twists","issue":"12","volume":156,"page":"2437-2468","type":"journal_article","publication":"Compositio Mathematica","publication_status":"published","citation":{"short":"M. Dimitrov, F. Januszewski, A. Raghuram, Compositio Mathematica 156 (2021) 2437–2468.","mla":"Dimitrov, Mladen, et al. “L-Functions of GL(2n): P-Adic Properties and Non-Vanishing of Twists.” Compositio Mathematica, vol. 156, no. 12, Wiley, 2021, pp. 2437–68, doi:10.1112/s0010437x20007551.","bibtex":"@article{Dimitrov_Januszewski_Raghuram_2021, title={L-functions of GL(2n): p-adic properties and non-vanishing of twists}, volume={156}, DOI={10.1112/s0010437x20007551}, number={12}, journal={Compositio Mathematica}, publisher={Wiley}, author={Dimitrov, Mladen and Januszewski, Fabian and Raghuram, A.}, year={2021}, pages={2437–2468} }","chicago":"Dimitrov, Mladen, Fabian Januszewski, and A. Raghuram. “L-Functions of GL(2n): P-Adic Properties and Non-Vanishing of Twists.” Compositio Mathematica 156, no. 12 (2021): 2437–68. https://doi.org/10.1112/s0010437x20007551.","ieee":"M. Dimitrov, F. Januszewski, and A. Raghuram, “L-functions of GL(2n): p-adic properties and non-vanishing of twists,” Compositio Mathematica, vol. 156, no. 12, pp. 2437–2468, 2021, doi: 10.1112/s0010437x20007551.","apa":"Dimitrov, M., Januszewski, F., & Raghuram, A. (2021). L-functions of GL(2n): p-adic properties and non-vanishing of twists. Compositio Mathematica, 156(12), 2437–2468. https://doi.org/10.1112/s0010437x20007551","ama":"Dimitrov M, Januszewski F, Raghuram A. L-functions of GL(2n): p-adic properties and non-vanishing of twists. Compositio Mathematica. 2021;156(12):2437-2468. doi:10.1112/s0010437x20007551"},"intvolume":" 156","author":[{"last_name":"Dimitrov","full_name":"Dimitrov, Mladen","first_name":"Mladen"},{"first_name":"Fabian","full_name":"Januszewski, Fabian","id":"81636","last_name":"Januszewski"},{"first_name":"A.","full_name":"Raghuram, A.","last_name":"Raghuram"}],"article_type":"original","date_updated":"2024-04-03T17:13:25Z","_id":"53192","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-437X","1570-5846"]},"year":"2021","publisher":"Wiley","date_created":"2024-04-03T16:58:55Z"},{"status":"public","year":"2021","publication_identifier":{"issn":["0025-5718","1088-6842"]},"language":[{"iso":"eng"}],"publisher":"American Mathematical Society (AMS)","date_created":"2022-12-22T10:48:44Z","date_updated":"2023-03-06T08:57:45Z","_id":"34840","intvolume":" 90","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Toru","full_name":"Komatsu, Toru","last_name":"Komatsu"}],"department":[{"_id":"102"}],"publication_status":"published","citation":{"short":"J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.","bibtex":"@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}, volume={90}, DOI={10.1090/mcom/3609}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497} }","mla":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” Mathematics of Computation, vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:10.1090/mcom/3609.","ieee":"J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class group of exponent $3$ and $5$,” Mathematics of Computation, vol. 90, no. 329, pp. 1483–1497, 2021, doi: 10.1090/mcom/3609.","chicago":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” Mathematics of Computation 90, no. 329 (2021): 1483–97. https://doi.org/10.1090/mcom/3609.","apa":"Klüners, J., & Komatsu, T. (2021). Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. Mathematics of Computation, 90(329), 1483–1497. https://doi.org/10.1090/mcom/3609","ama":"Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. Mathematics of Computation. 2021;90(329):1483-1497. doi:10.1090/mcom/3609"},"type":"journal_article","publication":"Mathematics of Computation","issue":"329","volume":90,"page":"1483-1497","abstract":[{"lang":"eng","text":"In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. "}],"doi":"10.1090/mcom/3609","title":"Imaginary multiquadratic number fields with class group of exponent $3$ and $5$","external_id":{"arxiv":["2004.03308v2"]},"user_id":"93826","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"]},{"issue":"333","page":"401-449","volume":91,"type":"journal_article","publication":"Mathematics of Computation","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"user_id":"93826","doi":"10.1090/mcom/3672","abstract":[{"lang":"eng","text":"Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. "}],"title":"Spanning the isogeny class of a power of an elliptic curve","date_updated":"2023-04-04T07:52:43Z","_id":"34912","language":[{"iso":"eng"}],"year":"2021","publication_identifier":{"issn":["0025-5718","1088-6842"]},"status":"public","date_created":"2022-12-23T11:02:02Z","publisher":"American Mathematical Society (AMS)","department":[{"_id":"102"}],"citation":{"short":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation 91 (2021) 401–449.","mla":"Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics of Computation, vol. 91, no. 333, American Mathematical Society (AMS), 2021, pp. 401–49, doi:10.1090/mcom/3672.","bibtex":"@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the isogeny class of a power of an elliptic curve}, volume={91}, DOI={10.1090/mcom/3672}, number={333}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}, year={2021}, pages={401–449} }","chicago":"Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics of Computation 91, no. 333 (2021): 401–49. https://doi.org/10.1090/mcom/3672.","ieee":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the isogeny class of a power of an elliptic curve,” Mathematics of Computation, vol. 91, no. 333, pp. 401–449, 2021, doi: 10.1090/mcom/3672.","apa":"Kirschmer, M., Narbonne, F., Ritzenthaler, C., & Robert, D. (2021). Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation, 91(333), 401–449. https://doi.org/10.1090/mcom/3672","ama":"Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation. 2021;91(333):401-449. doi:10.1090/mcom/3672"},"publication_status":"published","intvolume":" 91","author":[{"id":"82258","last_name":"Kirschmer","full_name":"Kirschmer, Markus","first_name":"Markus"},{"full_name":"Narbonne, Fabien","first_name":"Fabien","last_name":"Narbonne"},{"last_name":"Ritzenthaler","first_name":"Christophe","full_name":"Ritzenthaler, Christophe"},{"full_name":"Robert, Damien","first_name":"Damien","last_name":"Robert"}]},{"volume":20,"issue":"12","publication":"Journal of Algebra and Its Applications","type":"journal_article","user_id":"97359","keyword":["Applied Mathematics","Algebra and Number Theory"],"external_id":{"arxiv":["1906.02844"]},"extern":"1","title":"A new algorithm for computing idempotents of ℛ-trivial monoids","doi":"10.1142/s0219498821502273","abstract":[{"lang":"eng","text":"The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoid are equivalent to so-called weakly ordered monoids. We provide an alternative algorithm, based only on the simple observation that an R-trivial monoid may be realized by upper triangular matrices. This approach is inspired by results in the field of coupled cell network dynamical systems, where L-trivial monoids (the opposite notion) correspond to so-called feed-forward networks. We first show that our algorithm works for ZM, after which we prove that it also works for RM where R is an arbitrary ring with a known complete system of primitive orthogonal idempotents. In particular, our algorithm works if R is any field. In this respect our result constitutes a considerable generalization of the results in Berg et al. [J. Algebra 348 (2011) 446–461]. Moreover, the system of idempotents for RM is obtained from the one our algorithm yields for ZM in a straightforward manner. In other words, for any finite R-trivial monoid M our algorithm only has to be performed for ZM, after which a system of idempotents follows for any ring with a given system of idempotents."}],"_id":"33262","date_updated":"2022-09-07T08:35:24Z","publisher":"World Scientific Pub Co Pte Ltd","date_created":"2022-09-06T11:37:00Z","status":"public","publication_identifier":{"issn":["0219-4988","1793-6829"]},"year":"2020","language":[{"iso":"eng"}],"publication_status":"published","citation":{"mla":"Nijholt, Eddie, et al. “A New Algorithm for Computing Idempotents of ℛ-Trivial Monoids.” Journal of Algebra and Its Applications, vol. 20, no. 12, World Scientific Pub Co Pte Ltd, 2020, doi:10.1142/s0219498821502273.","bibtex":"@article{Nijholt_Rink_Schwenker_2020, title={A new algorithm for computing idempotents of ℛ-trivial monoids}, volume={20}, DOI={10.1142/s0219498821502273}, number={12}, journal={Journal of Algebra and Its Applications}, publisher={World Scientific Pub Co Pte Ltd}, author={Nijholt, Eddie and Rink, Bob and Schwenker, Sören}, year={2020} }","short":"E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications 20 (2020).","apa":"Nijholt, E., Rink, B., & Schwenker, S. (2020). A new algorithm for computing idempotents of ℛ-trivial monoids. Journal of Algebra and Its Applications, 20(12). https://doi.org/10.1142/s0219498821502273","ama":"Nijholt E, Rink B, Schwenker S. A new algorithm for computing idempotents of ℛ-trivial monoids. Journal of Algebra and Its Applications. 2020;20(12). doi:10.1142/s0219498821502273","chicago":"Nijholt, Eddie, Bob Rink, and Sören Schwenker. “A New Algorithm for Computing Idempotents of ℛ-Trivial Monoids.” Journal of Algebra and Its Applications 20, no. 12 (2020). https://doi.org/10.1142/s0219498821502273.","ieee":"E. Nijholt, B. Rink, and S. Schwenker, “A new algorithm for computing idempotents of ℛ-trivial monoids,” Journal of Algebra and Its Applications, vol. 20, no. 12, 2020, doi: 10.1142/s0219498821502273."},"author":[{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"last_name":"Rink","first_name":"Bob","full_name":"Rink, Bob"},{"full_name":"Schwenker, Sören","first_name":"Sören","last_name":"Schwenker","id":"97359","orcid":"0000-0002-8054-2058"}],"intvolume":" 20"},{"_id":"45955","date_updated":"2024-04-03T09:20:36Z","date_created":"2023-07-10T11:42:57Z","publisher":"American Mathematical Society (AMS)","year":"2020","publication_identifier":{"issn":["0025-5718","1088-6842"]},"language":[{"iso":"eng"}],"status":"public","citation":{"apa":"Akrivis, G., Feischl, M., Kovács, B., & Lubich, C. (2020). Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Mathematics of Computation, 90(329), 995–1038. https://doi.org/10.1090/mcom/3597","ama":"Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Mathematics of Computation. 2020;90(329):995-1038. doi:10.1090/mcom/3597","chicago":"Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” Mathematics of Computation 90, no. 329 (2020): 995–1038. https://doi.org/10.1090/mcom/3597.","ieee":"G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation,” Mathematics of Computation, vol. 90, no. 329, pp. 995–1038, 2020, doi: 10.1090/mcom/3597.","mla":"Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” Mathematics of Computation, vol. 90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:10.1090/mcom/3597.","bibtex":"@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90}, DOI={10.1090/mcom/3597}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}, year={2020}, pages={995–1038} }","short":"G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038."},"publication_status":"published","department":[{"_id":"841"}],"author":[{"first_name":"Georgios","full_name":"Akrivis, Georgios","last_name":"Akrivis"},{"first_name":"Michael","full_name":"Feischl, Michael","last_name":"Feischl"},{"orcid":"0000-0001-9872-3474","first_name":"Balázs","full_name":"Kovács, Balázs","last_name":"Kovács","id":"100441"},{"last_name":"Lubich","first_name":"Christian","full_name":"Lubich, Christian"}],"intvolume":" 90","page":"995-1038","volume":90,"issue":"329","publication":"Mathematics of Computation","type":"journal_article","user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"title":"Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation","doi":"10.1090/mcom/3597"},{"_id":"34842","date_updated":"2023-03-06T10:19:53Z","date_created":"2022-12-22T10:51:13Z","publisher":"Institute of Mathematics, Polish Academy of Sciences","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"year":"2020","status":"public","citation":{"ieee":"A.-S. Elsenhans, J. Klüners, and F. Nicolae, “Imaginary quadratic number fields with class groups of small exponent,” Acta Arithmetica, vol. 193, no. 3, pp. 217–233, 2020, doi: 10.4064/aa180220-20-3.","chicago":"Elsenhans, Andreas-Stephan, Jürgen Klüners, and Florin Nicolae. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” Acta Arithmetica 193, no. 3 (2020): 217–33. https://doi.org/10.4064/aa180220-20-3.","ama":"Elsenhans A-S, Klüners J, Nicolae F. Imaginary quadratic number fields with class groups of small exponent. Acta Arithmetica. 2020;193(3):217-233. doi:10.4064/aa180220-20-3","apa":"Elsenhans, A.-S., Klüners, J., & Nicolae, F. (2020). Imaginary quadratic number fields with class groups of small exponent. Acta Arithmetica, 193(3), 217–233. https://doi.org/10.4064/aa180220-20-3","short":"A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.","bibtex":"@article{Elsenhans_Klüners_Nicolae_2020, title={Imaginary quadratic number fields with class groups of small exponent}, volume={193}, DOI={10.4064/aa180220-20-3}, number={3}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}, year={2020}, pages={217–233} }","mla":"Elsenhans, Andreas-Stephan, et al. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” Acta Arithmetica, vol. 193, no. 3, Institute of Mathematics, Polish Academy of Sciences, 2020, pp. 217–33, doi:10.4064/aa180220-20-3."},"publication_status":"published","department":[{"_id":"102"}],"author":[{"first_name":"Andreas-Stephan","full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans"},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","last_name":"Klüners","id":"21202"},{"full_name":"Nicolae, Florin","first_name":"Florin","last_name":"Nicolae"}],"intvolume":" 193","page":"217-233","volume":193,"issue":"3","publication":"Acta Arithmetica","type":"journal_article","keyword":["Algebra and Number Theory"],"user_id":"93826","external_id":{"arxiv":["1803.02056 "]},"title":"Imaginary quadratic number fields with class groups of small exponent","doi":"10.4064/aa180220-20-3","abstract":[{"lang":"eng","text":"Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8."}]},{"place":"Bizerte, Tunisia","author":[{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"first_name":"Viviane","full_name":"Durand-Guerrier, Viviane","last_name":"Durand-Guerrier"}],"editor":[{"full_name":"Hausberger, T.","first_name":"T.","last_name":"Hausberger"},{"first_name":"M.","full_name":"Bosch, M.","last_name":"Bosch"},{"first_name":"F.","full_name":"Chelloughi, F.","last_name":"Chelloughi"}],"department":[{"_id":"363"}],"citation":{"apa":"Biehler, R., & Durand-Guerrier, V. (2020). University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic. In T. Hausberger, M. Bosch, & F. Chelloughi (Eds.), Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020) (pp. 283–287). University of Carthage and INDRUM.","ama":"Biehler R, Durand-Guerrier V. University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic. In: Hausberger T, Bosch M, Chelloughi F, eds. Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020). University of Carthage and INDRUM; 2020:283-287.","ieee":"R. Biehler and V. Durand-Guerrier, “University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic,” in Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020), T. Hausberger, M. Bosch, and F. Chelloughi, Eds. Bizerte, Tunisia: University of Carthage and INDRUM, 2020, pp. 283–287.","chicago":"Biehler, Rolf, and Viviane Durand-Guerrier. “University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic.” In Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020), edited by T. Hausberger, M. Bosch, and F. Chelloughi, 283–87. Bizerte, Tunisia: University of Carthage and INDRUM, 2020.","bibtex":"@inbook{Biehler_Durand-Guerrier_2020, place={Bizerte, Tunisia}, title={University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic}, booktitle={Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)}, publisher={University of Carthage and INDRUM}, author={Biehler, Rolf and Durand-Guerrier, Viviane}, editor={Hausberger, T. and Bosch, M. and Chelloughi, F.}, year={2020}, pages={283–287} }","mla":"Biehler, Rolf, and Viviane Durand-Guerrier. “University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic.” Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020), edited by T. Hausberger et al., University of Carthage and INDRUM, 2020, pp. 283–87.","short":"R. Biehler, V. Durand-Guerrier, in: T. Hausberger, M. Bosch, F. Chelloughi (Eds.), Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020), University of Carthage and INDRUM, Bizerte, Tunisia, 2020, pp. 283–287."},"language":[{"iso":"eng"}],"year":"2020","status":"public","related_material":{"link":[{"relation":"confirmation","url":"https://hal.science/hal-03114041/"}]},"date_created":"2023-01-10T11:14:02Z","publisher":"University of Carthage and INDRUM","date_updated":"2024-11-11T11:59:12Z","_id":"35811","file_date_updated":"2024-11-11T11:58:37Z","has_accepted_license":"1","title":"University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic","file":[{"date_created":"2024-11-11T11:58:37Z","access_level":"closed","content_type":"application/pdf","file_id":"56978","file_size":576039,"file_name":"Biehler_INDRUM2020_283-287.pdf","creator":"krueter","success":1,"relation":"main_file","date_updated":"2024-11-11T11:58:37Z"}],"main_file_link":[{"url":"⟨hal-03114041⟩"}],"keyword":["Number Theory","Algebra","Discrete Mathematics","Logic","Research in University Mathematics Edcuation"],"user_id":"37888","type":"book_chapter","publication":"Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)","ddc":["510"],"page":"283-287"},{"type":"journal_article","publication":"Journal of Number Theory","page":"311-322","volume":212,"abstract":[{"text":"We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant.\r\n","lang":"eng"}],"doi":"10.1016/j.jnt.2019.11.007","title":"The conductor density of local function fields with abelian Galois group","external_id":{"arxiv":["1904.02573 "]},"user_id":"82981","keyword":["Algebra and Number Theory"],"publication_identifier":{"issn":["0022-314X"]},"year":"2020","language":[{"iso":"eng"}],"status":"public","date_created":"2022-12-22T10:50:03Z","publisher":"Elsevier BV","date_updated":"2025-06-13T08:18:30Z","_id":"34841","intvolume":" 212","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"full_name":"Müller, Raphael","first_name":"Raphael","last_name":"Müller"}],"department":[{"_id":"102"}],"citation":{"ama":"Klüners J, Müller R. The conductor density of local function fields with abelian Galois group. Journal of Number Theory. 2020;212:311-322. doi:10.1016/j.jnt.2019.11.007","apa":"Klüners, J., & Müller, R. (2020). The conductor density of local function fields with abelian Galois group. Journal of Number Theory, 212, 311–322. https://doi.org/10.1016/j.jnt.2019.11.007","chicago":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” Journal of Number Theory 212 (2020): 311–22. https://doi.org/10.1016/j.jnt.2019.11.007.","ieee":"J. Klüners and R. Müller, “The conductor density of local function fields with abelian Galois group,” Journal of Number Theory, vol. 212, pp. 311–322, 2020, doi: 10.1016/j.jnt.2019.11.007.","mla":"Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function Fields with Abelian Galois Group.” Journal of Number Theory, vol. 212, Elsevier BV, 2020, pp. 311–22, doi:10.1016/j.jnt.2019.11.007.","bibtex":"@article{Klüners_Müller_2020, title={The conductor density of local function fields with abelian Galois group}, volume={212}, DOI={10.1016/j.jnt.2019.11.007}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }","short":"J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322."},"publication_status":"published"},{"volume":15,"page":"309-325","issue":"02","publication":"International Journal of Number Theory","type":"journal_article","user_id":"82258","keyword":["Algebra and Number Theory"],"title":"Quaternary quadratic lattices over number fields","abstract":[{"text":"We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).","lang":"eng"}],"doi":"10.1142/s1793042119500131","_id":"34917","date_updated":"2023-12-06T10:05:59Z","publisher":"World Scientific Pub Co Pte Lt","date_created":"2022-12-23T11:05:09Z","status":"public","publication_identifier":{"issn":["1793-0421","1793-7310"]},"year":"2019","language":[{"iso":"eng"}],"publication_status":"published","citation":{"chicago":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” International Journal of Number Theory 15, no. 02 (2019): 309–25. https://doi.org/10.1142/s1793042119500131.","ieee":"M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,” International Journal of Number Theory, vol. 15, no. 02, pp. 309–325, 2019, doi: 10.1142/s1793042119500131.","ama":"Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. International Journal of Number Theory. 2019;15(02):309-325. doi:10.1142/s1793042119500131","apa":"Kirschmer, M., & Nebe, G. (2019). Quaternary quadratic lattices over number fields. International Journal of Number Theory, 15(02), 309–325. https://doi.org/10.1142/s1793042119500131","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.","mla":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” International Journal of Number Theory, vol. 15, no. 02, World Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:10.1142/s1793042119500131.","bibtex":"@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over number fields}, volume={15}, DOI={10.1142/s1793042119500131}, number={02}, journal={International Journal of Number Theory}, publisher={World Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019}, pages={309–325} }"},"department":[{"_id":"102"}],"author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"last_name":"Nebe","full_name":"Nebe, Gabriele","first_name":"Gabriele"}],"intvolume":" 15"},{"_id":"34916","date_updated":"2023-12-06T10:07:17Z","publisher":"Elsevier BV","date_created":"2022-12-23T11:04:34Z","status":"public","year":"2019","publication_identifier":{"issn":["0022-314X"]},"language":[{"iso":"eng"}],"publication_status":"published","citation":{"short":"M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.","mla":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” Journal of Number Theory, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:10.1016/j.jnt.2018.08.004.","bibtex":"@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices over number fields}, volume={197}, DOI={10.1016/j.jnt.2018.08.004}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2019}, pages={121–134} }","chicago":"Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.” Journal of Number Theory 197 (2019): 121–34. https://doi.org/10.1016/j.jnt.2018.08.004.","ieee":"M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,” Journal of Number Theory, vol. 197, pp. 121–134, 2019, doi: 10.1016/j.jnt.2018.08.004.","apa":"Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number fields. Journal of Number Theory, 197, 121–134. https://doi.org/10.1016/j.jnt.2018.08.004","ama":"Kirschmer M. Automorphisms of even unimodular lattices over number fields. Journal of Number Theory. 2019;197:121-134. doi:10.1016/j.jnt.2018.08.004"},"department":[{"_id":"102"}],"author":[{"id":"82258","last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus"}],"intvolume":" 197","volume":197,"page":"121-134","publication":"Journal of Number Theory","type":"journal_article","user_id":"82258","keyword":["Algebra and Number Theory"],"title":"Automorphisms of even unimodular lattices over number fields","abstract":[{"lang":"eng","text":"We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman."}],"doi":"10.1016/j.jnt.2018.08.004"},{"intvolume":" 93","author":[{"full_name":"Elsenhans, Andreas-Stephan","first_name":"Andreas-Stephan","last_name":"Elsenhans"},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","last_name":"Klüners","id":"21202"}],"department":[{"_id":"102"}],"publication_status":"published","citation":{"mla":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” Journal of Symbolic Computation, vol. 93, Elsevier BV, 2018, pp. 1–20, doi:10.1016/j.jsc.2018.04.013.","bibtex":"@article{Elsenhans_Klüners_2018, title={Computing subfields of number fields and applications to Galois group computations}, volume={93}, DOI={10.1016/j.jsc.2018.04.013}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2018}, pages={1–20} }","short":"A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20.","apa":"Elsenhans, A.-S., & Klüners, J. (2018). Computing subfields of number fields and applications to Galois group computations. Journal of Symbolic Computation, 93, 1–20. https://doi.org/10.1016/j.jsc.2018.04.013","ama":"Elsenhans A-S, Klüners J. Computing subfields of number fields and applications to Galois group computations. Journal of Symbolic Computation. 2018;93:1-20. doi:10.1016/j.jsc.2018.04.013","chicago":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” Journal of Symbolic Computation 93 (2018): 1–20. https://doi.org/10.1016/j.jsc.2018.04.013.","ieee":"A.-S. Elsenhans and J. Klüners, “Computing subfields of number fields and applications to Galois group computations,” Journal of Symbolic Computation, vol. 93, pp. 1–20, 2018, doi: 10.1016/j.jsc.2018.04.013."},"status":"public","publication_identifier":{"issn":["0747-7171"]},"year":"2018","language":[{"iso":"eng"}],"publisher":"Elsevier BV","date_created":"2022-12-22T10:52:18Z","date_updated":"2023-03-06T09:05:51Z","_id":"34843","abstract":[{"lang":"eng","text":"A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013).\r\n\r\nThis article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields. In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method from van Hoeij et al. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields.\r\n\r\nFinally, we explain how we use subfields to get a good starting group for the computation of Galois groups."}],"doi":"10.1016/j.jsc.2018.04.013","title":"Computing subfields of number fields and applications to Galois group computations","external_id":{"arxiv":["1610.06837 "]},"user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"],"type":"journal_article","publication":"Journal of Symbolic Computation","volume":93,"page":"1-20"},{"volume":30,"page":"847-857","issue":"3","publication":"Journal de Théorie des Nombres de Bordeaux","type":"journal_article","keyword":["Algebra and Number Theory"],"user_id":"93826","extern":"1","title":"One-class genera of exceptional groups over number fields","doi":"10.5802/jtnb.1052","abstract":[{"lang":"eng","text":"We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G₂ . For the group G₂, we enumerate all such one-class genera for the usual seven-dimensional representation."}],"_id":"42790","date_updated":"2023-04-04T09:07:32Z","publisher":"Cellule MathDoc/CEDRAM","date_created":"2023-03-07T08:27:36Z","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1246-7405","2118-8572"]},"year":"2018","publication_status":"published","citation":{"bibtex":"@article{Kirschmer_2018, title={One-class genera of exceptional groups over number fields}, volume={30}, DOI={10.5802/jtnb.1052}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Kirschmer, Markus}, year={2018}, pages={847–857} }","mla":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” Journal de Théorie Des Nombres de Bordeaux, vol. 30, no. 3, Cellule MathDoc/CEDRAM, 2018, pp. 847–57, doi:10.5802/jtnb.1052.","short":"M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857.","ama":"Kirschmer M. One-class genera of exceptional groups over number fields. Journal de Théorie des Nombres de Bordeaux. 2018;30(3):847-857. doi:10.5802/jtnb.1052","apa":"Kirschmer, M. (2018). One-class genera of exceptional groups over number fields. Journal de Théorie Des Nombres de Bordeaux, 30(3), 847–857. https://doi.org/10.5802/jtnb.1052","ieee":"M. Kirschmer, “One-class genera of exceptional groups over number fields,” Journal de Théorie des Nombres de Bordeaux, vol. 30, no. 3, pp. 847–857, 2018, doi: 10.5802/jtnb.1052.","chicago":"Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.” Journal de Théorie Des Nombres de Bordeaux 30, no. 3 (2018): 847–57. https://doi.org/10.5802/jtnb.1052."},"department":[{"_id":"102"}],"author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"}],"intvolume":" 30"},{"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"}],"citation":{"bibtex":"@inproceedings{Lass_Mohr_Wiebeler_Kühne_Plessl_2018, place={New York, NY, USA}, title={A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices}, DOI={10.1145/3218176.3218231}, booktitle={Proc. Platform for Advanced Scientific Computing (PASC) Conference}, publisher={ACM}, author={Lass, Michael and Mohr, Stephan and Wiebeler, Hendrik and Kühne, Thomas and Plessl, Christian}, year={2018} }","mla":"Lass, Michael, et al. “A Massively Parallel Algorithm for the Approximate Calculation of Inverse P-Th Roots of Large Sparse Matrices.” Proc. Platform for Advanced Scientific Computing (PASC) Conference, ACM, 2018, doi:10.1145/3218176.3218231.","short":"M. Lass, S. Mohr, H. Wiebeler, T. Kühne, C. Plessl, in: Proc. Platform for Advanced Scientific Computing (PASC) Conference, ACM, New York, NY, USA, 2018.","ama":"Lass M, Mohr S, Wiebeler H, Kühne T, Plessl C. A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices. In: Proc. Platform for Advanced Scientific Computing (PASC) Conference. ACM; 2018. doi:10.1145/3218176.3218231","apa":"Lass, M., Mohr, S., Wiebeler, H., Kühne, T., & Plessl, C. (2018). A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices. Proc. Platform for Advanced Scientific Computing (PASC) Conference. Platform for Advanced Scientific Computing Conference (PASC), Basel, Switzerland. https://doi.org/10.1145/3218176.3218231","ieee":"M. Lass, S. Mohr, H. Wiebeler, T. Kühne, and C. Plessl, “A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices,” presented at the Platform for Advanced Scientific Computing Conference (PASC), Basel, Switzerland, 2018, doi: 10.1145/3218176.3218231.","chicago":"Lass, Michael, Stephan Mohr, Hendrik Wiebeler, Thomas Kühne, and Christian Plessl. “A Massively Parallel Algorithm for the Approximate Calculation of Inverse P-Th Roots of Large Sparse Matrices.” In Proc. Platform for Advanced Scientific Computing (PASC) Conference. New York, NY, USA: ACM, 2018. https://doi.org/10.1145/3218176.3218231."},"place":"New York, NY, USA","conference":{"start_date":"2018-07-02","location":"Basel, Switzerland","name":"Platform for Advanced Scientific Computing Conference (PASC)","end_date":"2018-07-04"},"author":[{"last_name":"Lass","id":"24135","first_name":"Michael","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632"},{"full_name":"Mohr, Stephan","first_name":"Stephan","last_name":"Mohr"},{"full_name":"Wiebeler, Hendrik","first_name":"Hendrik","last_name":"Wiebeler"},{"full_name":"Kühne, Thomas","first_name":"Thomas","last_name":"Kühne","id":"49079"},{"orcid":"0000-0001-5728-9982","last_name":"Plessl","id":"16153","full_name":"Plessl, Christian","first_name":"Christian"}],"date_updated":"2023-09-26T11:48:12Z","_id":"1590","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-1-4503-5891-0/18/07"]},"year":"2018","status":"public","date_created":"2018-03-22T10:53:01Z","publisher":"ACM","external_id":{"arxiv":["1710.10899"]},"keyword":["approximate computing","linear algebra","matrix inversion","matrix p-th roots","numeric algorithm","parallel computing"],"user_id":"15278","project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1 / 320898746"},{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"abstract":[{"lang":"eng","text":"We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. Following the idea of Approximate Computing, we allow imprecision in the final result in order to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures.\r\n\r\nWe evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution."}],"doi":"10.1145/3218176.3218231","title":"A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices","type":"conference","publication":"Proc. Platform for Advanced Scientific Computing (PASC) Conference","quality_controlled":"1"},{"author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer","id":"82258"},{"full_name":"Rüther, Marion G.","first_name":"Marion G.","last_name":"Rüther"}],"intvolume":" 480","citation":{"ama":"Kirschmer M, Rüther MG. The constructive membership problem for discrete two-generator subgroups of SL(2,R). Journal of Algebra. 2017;480:519-548. doi:10.1016/j.jalgebra.2017.02.029","bibtex":"@article{Kirschmer_Rüther_2017, title={The constructive membership problem for discrete two-generator subgroups of SL(2,R)}, volume={480}, DOI={10.1016/j.jalgebra.2017.02.029}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Kirschmer, Markus and Rüther, Marion G.}, year={2017}, pages={519–548} }","apa":"Kirschmer, M., & Rüther, M. G. (2017). The constructive membership problem for discrete two-generator subgroups of SL(2,R). Journal of Algebra, 480, 519–548. https://doi.org/10.1016/j.jalgebra.2017.02.029","mla":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” Journal of Algebra, vol. 480, Elsevier BV, 2017, pp. 519–48, doi:10.1016/j.jalgebra.2017.02.029.","ieee":"M. Kirschmer and M. G. Rüther, “The constructive membership problem for discrete two-generator subgroups of SL(2,R),” Journal of Algebra, vol. 480, pp. 519–548, 2017, doi: 10.1016/j.jalgebra.2017.02.029.","short":"M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548.","chicago":"Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem for Discrete Two-Generator Subgroups of SL(2,R).” Journal of Algebra 480 (2017): 519–48. https://doi.org/10.1016/j.jalgebra.2017.02.029."},"publication_status":"published","department":[{"_id":"102"}],"date_created":"2023-03-07T08:28:11Z","publisher":"Elsevier BV","language":[{"iso":"eng"}],"year":"2017","publication_identifier":{"issn":["0021-8693"]},"status":"public","_id":"42791","date_updated":"2023-04-04T09:10:14Z","title":"The constructive membership problem for discrete two-generator subgroups of SL(2,R)","extern":"1","abstract":[{"text":"We describe a practical algorithm to solve the constructive membership problem for discrete two-generator subgroups of SL₂(R) or PSL₂(R). This algorithm has been implemented in Magma for groups defined over real algebraic number fields.","lang":"eng"}],"doi":"10.1016/j.jalgebra.2017.02.029","keyword":["Algebra and Number Theory"],"user_id":"93826","publication":"Journal of Algebra","type":"journal_article","page":"519-548","volume":480},{"publication":"Journal of Number Theory","type":"journal_article","page":"161-168","volume":167,"title":"Are number fields determined by Artin L-functions?","abstract":[{"lang":"eng","text":"Let k be a number field, K/k a finite Galois extension with Galois group G, χ a faithful character of G. We prove that the Artin L-function L(s,χ,K/k) determines the Galois closure of K over $\\ℚ$. In the special case $k=\\ℚ$ it also determines the character χ. "}],"doi":"10.1016/j.jnt.2016.03.023","keyword":["Algebra and Number Theory"],"user_id":"93826","external_id":{"arxiv":["1509.06883 "]},"date_created":"2022-12-22T10:52:47Z","publisher":"Elsevier BV","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-314X"]},"year":"2016","status":"public","_id":"34844","date_updated":"2023-03-06T10:44:22Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Florin","full_name":"Nicolae, Florin","last_name":"Nicolae"}],"intvolume":" 167","citation":{"bibtex":"@article{Klüners_Nicolae_2016, title={Are number fields determined by Artin L-functions?}, volume={167}, DOI={10.1016/j.jnt.2016.03.023}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners, Jürgen and Nicolae, Florin}, year={2016}, pages={161–168} }","mla":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” Journal of Number Theory, vol. 167, Elsevier BV, 2016, pp. 161–68, doi:10.1016/j.jnt.2016.03.023.","short":"J. Klüners, F. Nicolae, Journal of Number Theory 167 (2016) 161–168.","apa":"Klüners, J., & Nicolae, F. (2016). Are number fields determined by Artin L-functions? Journal of Number Theory, 167, 161–168. https://doi.org/10.1016/j.jnt.2016.03.023","ama":"Klüners J, Nicolae F. Are number fields determined by Artin L-functions? Journal of Number Theory. 2016;167:161-168. doi:10.1016/j.jnt.2016.03.023","ieee":"J. Klüners and F. Nicolae, “Are number fields determined by Artin L-functions?,” Journal of Number Theory, vol. 167, pp. 161–168, 2016, doi: 10.1016/j.jnt.2016.03.023.","chicago":"Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin L-Functions?” Journal of Number Theory 167 (2016): 161–68. https://doi.org/10.1016/j.jnt.2016.03.023."},"publication_status":"published","department":[{"_id":"102"}]},{"type":"journal_article","publication":"Journal of Number Theory","volume":161,"page":"343-361","abstract":[{"text":"We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.","lang":"eng"}],"doi":"10.1016/j.jnt.2014.11.001","extern":"1","title":"Ternary quadratic forms over number fields with small class number","keyword":["Algebra and Number Theory"],"user_id":"93826","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-314X"]},"year":"2016","publisher":"Elsevier BV","date_created":"2023-03-07T08:28:46Z","date_updated":"2023-04-04T09:10:42Z","_id":"42792","intvolume":" 161","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer","id":"82258"},{"last_name":"Lorch","first_name":"David","full_name":"Lorch, David"}],"department":[{"_id":"102"}],"publication_status":"published","citation":{"ama":"Kirschmer M, Lorch D. Ternary quadratic forms over number fields with small class number. Journal of Number Theory. 2016;161:343-361. doi:10.1016/j.jnt.2014.11.001","apa":"Kirschmer, M., & Lorch, D. (2016). Ternary quadratic forms over number fields with small class number. Journal of Number Theory, 161, 343–361. https://doi.org/10.1016/j.jnt.2014.11.001","chicago":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” Journal of Number Theory 161 (2016): 343–61. https://doi.org/10.1016/j.jnt.2014.11.001.","ieee":"M. Kirschmer and D. Lorch, “Ternary quadratic forms over number fields with small class number,” Journal of Number Theory, vol. 161, pp. 343–361, 2016, doi: 10.1016/j.jnt.2014.11.001.","mla":"Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields with Small Class Number.” Journal of Number Theory, vol. 161, Elsevier BV, 2016, pp. 343–61, doi:10.1016/j.jnt.2014.11.001.","bibtex":"@article{Kirschmer_Lorch_2016, title={Ternary quadratic forms over number fields with small class number}, volume={161}, DOI={10.1016/j.jnt.2014.11.001}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus and Lorch, David}, year={2016}, pages={343–361} }","short":"M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361."}},{"author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","id":"82258","last_name":"Kirschmer"}],"intvolume":" 136","citation":{"ieee":"M. Kirschmer, “One-class genera of maximal integral quadratic forms,” Journal of Number Theory, vol. 136, pp. 375–393, 2014, doi: 10.1016/j.jnt.2013.10.007.","chicago":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” Journal of Number Theory 136 (2014): 375–93. https://doi.org/10.1016/j.jnt.2013.10.007.","short":"M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.","bibtex":"@article{Kirschmer_2014, title={One-class genera of maximal integral quadratic forms}, volume={136}, DOI={10.1016/j.jnt.2013.10.007}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer, Markus}, year={2014}, pages={375–393} }","ama":"Kirschmer M. One-class genera of maximal integral quadratic forms. Journal of Number Theory. 2014;136:375-393. doi:10.1016/j.jnt.2013.10.007","apa":"Kirschmer, M. (2014). One-class genera of maximal integral quadratic forms. Journal of Number Theory, 136, 375–393. https://doi.org/10.1016/j.jnt.2013.10.007","mla":"Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.” Journal of Number Theory, vol. 136, Elsevier BV, 2014, pp. 375–93, doi:10.1016/j.jnt.2013.10.007."},"publication_status":"published","department":[{"_id":"102"}],"date_created":"2023-03-07T08:29:34Z","publisher":"Elsevier BV","publication_identifier":{"issn":["0022-314X"]},"year":"2014","language":[{"iso":"eng"}],"status":"public","_id":"42793","date_updated":"2023-04-04T09:13:29Z","title":"One-class genera of maximal integral quadratic forms","extern":"1","doi":"10.1016/j.jnt.2013.10.007","abstract":[{"text":"Suppose Q is a definite quadratic form on a vector space V over some totally real field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 471 such genera. Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively. This classification also yields all maximal quaternion orders of type number one.","lang":"eng"}],"user_id":"93826","keyword":["Algebra and Number Theory"],"publication":"Journal of Number Theory","type":"journal_article","page":"375-393","volume":136},{"type":"journal_article","publication":"Compositio Mathematica","issue":"8","volume":149,"page":"1381-1400","doi":"10.1112/s0010437x13007045","abstract":[{"lang":"eng","text":"AbstractLet ${F}_{BC} (\\lambda , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $\\rho (k)$ of positive roots. We prove that ${F}_{BC} (\\lambda + \\rho (k), k; t)$ converges as ${k}_{1} + {k}_{2} \\rightarrow \\infty $ and ${k}_{1} / {k}_{2} \\rightarrow \\infty $ to a function of type A for $t\\in { \\mathbb{R} }^{n} $ and $\\lambda \\in { \\mathbb{C} }^{n} $. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits include limit transitions for the spherical functions of non-compact Grassmann manifolds over one of the fields $ \\mathbb{F} = \\mathbb{R} , \\mathbb{C} , \\mathbb{H} $ when the rank is fixed and the dimension tends to infinity. The limit functions turn out to be exactly the spherical functions of the corresponding infinite-dimensional Grassmann manifold in the sense of Olshanski."}],"title":"Limit transition between hypergeometric functions of type BC and type A","keyword":["Algebra and Number Theory"],"user_id":"93826","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-437X","1570-5846"]},"year":"2013","publisher":"Wiley","date_created":"2023-01-20T09:37:16Z","date_updated":"2023-01-24T22:15:13Z","_id":"37672","intvolume":" 149","author":[{"full_name":"Rösler, Margit","first_name":"Margit","last_name":"Rösler","id":"37390"},{"last_name":"Koornwinder","first_name":"Tom","full_name":"Koornwinder, Tom"},{"last_name":"Voit","full_name":"Voit, Michael","first_name":"Michael"}],"department":[{"_id":"555"}],"publication_status":"published","citation":{"bibtex":"@article{Rösler_Koornwinder_Voit_2013, title={Limit transition between hypergeometric functions of type BC and type A}, volume={149}, DOI={10.1112/s0010437x13007045}, number={8}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit and Koornwinder, Tom and Voit, Michael}, year={2013}, pages={1381–1400} }","mla":"Rösler, Margit, et al. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica, vol. 149, no. 8, Wiley, 2013, pp. 1381–400, doi:10.1112/s0010437x13007045.","short":"M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.","ama":"Rösler M, Koornwinder T, Voit M. Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica. 2013;149(8):1381-1400. doi:10.1112/s0010437x13007045","apa":"Rösler, M., Koornwinder, T., & Voit, M. (2013). Limit transition between hypergeometric functions of type BC and type A. Compositio Mathematica, 149(8), 1381–1400. https://doi.org/10.1112/s0010437x13007045","ieee":"M. Rösler, T. Koornwinder, and M. Voit, “Limit transition between hypergeometric functions of type BC and type A,” Compositio Mathematica, vol. 149, no. 8, pp. 1381–1400, 2013, doi: 10.1112/s0010437x13007045.","chicago":"Rösler, Margit, Tom Koornwinder, and Michael Voit. “Limit Transition between Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica 149, no. 8 (2013): 1381–1400. https://doi.org/10.1112/s0010437x13007045."}},{"date_updated":"2023-04-04T09:22:22Z","_id":"42797","status":"public","publication_identifier":{"issn":["0025-5718","1088-6842"]},"year":"2012","language":[{"iso":"eng"}],"publisher":"American Mathematical Society (AMS)","date_created":"2023-03-07T08:35:56Z","department":[{"_id":"102"}],"publication_status":"published","citation":{"mla":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” Mathematics of Computation, vol. 81, no. 279, American Mathematical Society (AMS), 2012, pp. 1619–34, doi:10.1090/s0025-5718-2011-02570-6.","bibtex":"@article{Kirschmer_2012, title={A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$}, volume={81}, DOI={10.1090/s0025-5718-2011-02570-6}, number={279}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus}, year={2012}, pages={1619–1634} }","short":"M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634.","ama":"Kirschmer M. A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. Mathematics of Computation. 2012;81(279):1619-1634. doi:10.1090/s0025-5718-2011-02570-6","apa":"Kirschmer, M. (2012). A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. Mathematics of Computation, 81(279), 1619–1634. https://doi.org/10.1090/s0025-5718-2011-02570-6","chicago":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” Mathematics of Computation 81, no. 279 (2012): 1619–34. https://doi.org/10.1090/s0025-5718-2011-02570-6.","ieee":"M. Kirschmer, “A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$,” Mathematics of Computation, vol. 81, no. 279, pp. 1619–1634, 2012, doi: 10.1090/s0025-5718-2011-02570-6."},"intvolume":" 81","author":[{"last_name":"Kirschmer","id":"82258","first_name":"Markus","full_name":"Kirschmer, Markus"}],"issue":"279","volume":81,"page":"1619-1634","type":"journal_article","publication":"Mathematics of Computation","user_id":"93826","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"abstract":[{"lang":"eng","text":"An efficient algorithm to compute automorphism groups and isometries of definite Fq[t]-lattices for odd q is presented. The algorithm requires several square root computations in Fq₂ but no enumeration of orbits having more than eight elements. "}],"doi":"10.1090/s0025-5718-2011-02570-6","extern":"1","title":"A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$"}]