--- _id: '34835' abstract: - lang: eng text: 'We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. ' author: - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners citation: ama: Klüners J. The asymptotics of nilpotent Galois groups. Acta Arithmetica. 2022;204(2):165-184. doi:10.4064/aa211207-16-5 apa: Klüners, J. (2022). The asymptotics of nilpotent Galois groups. Acta Arithmetica, 204(2), 165–184. https://doi.org/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} }' 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.' 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. short: J. Klüners, Acta Arithmetica 204 (2022) 165–184. date_created: 2022-12-22T10:08:23Z date_updated: 2023-03-06T08:48:33Z department: - _id: '102' doi: 10.4064/aa211207-16-5 external_id: arxiv: - '2011.04325 ' intvolume: ' 204' issue: '2' keyword: - Algebra and Number Theory language: - iso: eng page: 165-184 publication: Acta Arithmetica publication_identifier: issn: - 0065-1036 - 1730-6264 publication_status: published publisher: Institute of Mathematics, Polish Academy of Sciences status: public title: The asymptotics of nilpotent Galois groups type: journal_article user_id: '93826' volume: 204 year: '2022' ... --- _id: '53192' abstract: - lang: eng text: The principal aim of this article is to attach and study

$p$

-adic

$L$

-functions to cohomological cuspidal automorphic representations

$\Pi$

$\operatorname {GL}_{2n}$

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

$\chi$

$p$

-power conductor. article_type: original author: - first_name: Mladen full_name: Dimitrov, Mladen last_name: Dimitrov - first_name: Fabian full_name: Januszewski, Fabian id: '81636' last_name: Januszewski - first_name: A. full_name: Raghuram, A. last_name: Raghuram citation: 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' 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' 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.' 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.' short: M. Dimitrov, F. Januszewski, A. Raghuram, Compositio Mathematica 156 (2021) 2437–2468. date_created: 2024-04-03T16:58:55Z date_updated: 2024-04-03T17:13:25Z doi: 10.1112/s0010437x20007551 intvolume: ' 156' issue: '12' keyword: - Algebra and Number Theory language: - iso: eng page: 2437-2468 publication: Compositio Mathematica publication_identifier: issn: - 0010-437X - 1570-5846 publication_status: published publisher: Wiley status: public title: 'L-functions of GL(2n): p-adic properties and non-vanishing of twists' type: journal_article user_id: '81636' volume: 156 year: '2021' ... --- _id: '34840' 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. ' author: - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners - first_name: Toru full_name: Komatsu, Toru last_name: Komatsu citation: 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 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 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} }' 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.' 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.' 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. short: J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497. date_created: 2022-12-22T10:48:44Z date_updated: 2023-03-06T08:57:45Z department: - _id: '102' doi: 10.1090/mcom/3609 external_id: arxiv: - 2004.03308v2 intvolume: ' 90' issue: '329' keyword: - Applied Mathematics - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 1483-1497 publication: Mathematics of Computation publication_identifier: issn: - 0025-5718 - 1088-6842 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Imaginary multiquadratic number fields with class group of exponent $3$ and $5$ type: journal_article user_id: '93826' volume: 90 year: '2021' ... --- _id: '34912' 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. ' author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer - first_name: Fabien full_name: Narbonne, Fabien last_name: Narbonne - first_name: Christophe full_name: Ritzenthaler, Christophe last_name: Ritzenthaler - first_name: Damien full_name: Robert, Damien last_name: Robert citation: 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 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 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.' 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. short: M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation 91 (2021) 401–449. date_created: 2022-12-23T11:02:02Z date_updated: 2023-04-04T07:52:43Z department: - _id: '102' doi: 10.1090/mcom/3672 intvolume: ' 91' issue: '333' keyword: - Applied Mathematics - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 401-449 publication: Mathematics of Computation publication_identifier: issn: - 0025-5718 - 1088-6842 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Spanning the isogeny class of a power of an elliptic curve type: journal_article user_id: '93826' volume: 91 year: '2021' ... --- _id: '33262' 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. author: - first_name: Eddie full_name: Nijholt, Eddie last_name: Nijholt - first_name: Bob full_name: Rink, Bob last_name: Rink - first_name: Sören full_name: Schwenker, Sören id: '97359' last_name: Schwenker orcid: 0000-0002-8054-2058 citation: 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 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 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} }' 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.' 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. short: E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications 20 (2020). date_created: 2022-09-06T11:37:00Z date_updated: 2022-09-07T08:35:24Z doi: 10.1142/s0219498821502273 extern: '1' external_id: arxiv: - '1906.02844' intvolume: ' 20' issue: '12' keyword: - Applied Mathematics - Algebra and Number Theory language: - iso: eng publication: Journal of Algebra and Its Applications publication_identifier: issn: - 0219-4988 - 1793-6829 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: A new algorithm for computing idempotents of ℛ-trivial monoids type: journal_article user_id: '97359' volume: 20 year: '2020' ... --- _id: '45955' author: - first_name: Georgios full_name: Akrivis, Georgios last_name: Akrivis - first_name: Michael full_name: Feischl, Michael last_name: Feischl - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Christian full_name: Lubich, Christian last_name: Lubich citation: 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 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 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} }' 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. short: G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038. date_created: 2023-07-10T11:42:57Z date_updated: 2024-04-03T09:20:36Z department: - _id: '841' doi: 10.1090/mcom/3597 intvolume: ' 90' issue: '329' keyword: - Applied Mathematics - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 995-1038 publication: Mathematics of Computation publication_identifier: issn: - 0025-5718 - 1088-6842 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation type: journal_article user_id: '100441' volume: 90 year: '2020' ... --- _id: '34842' 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. author: - first_name: Andreas-Stephan full_name: Elsenhans, Andreas-Stephan last_name: Elsenhans - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners - first_name: Florin full_name: Nicolae, Florin last_name: Nicolae citation: 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 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} }' 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.' 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.' 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. short: A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233. date_created: 2022-12-22T10:51:13Z date_updated: 2023-03-06T10:19:53Z department: - _id: '102' doi: 10.4064/aa180220-20-3 external_id: arxiv: - '1803.02056 ' intvolume: ' 193' issue: '3' keyword: - Algebra and Number Theory language: - iso: eng page: 217-233 publication: Acta Arithmetica publication_identifier: issn: - 0065-1036 - 1730-6264 publication_status: published publisher: Institute of Mathematics, Polish Academy of Sciences status: public title: Imaginary quadratic number fields with class groups of small exponent type: journal_article user_id: '93826' volume: 193 year: '2020' ... --- _id: '35811' author: - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler - first_name: Viviane full_name: Durand-Guerrier, Viviane last_name: Durand-Guerrier citation: 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.' 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. 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} }' 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.' 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.' 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.' date_created: 2023-01-10T11:14:02Z date_updated: 2024-11-11T11:59:12Z ddc: - '510' department: - _id: '363' editor: - first_name: T. full_name: Hausberger, T. last_name: Hausberger - first_name: M. full_name: Bosch, M. last_name: Bosch - first_name: F. full_name: Chelloughi, F. last_name: Chelloughi file: - access_level: closed content_type: application/pdf creator: krueter date_created: 2024-11-11T11:58:37Z date_updated: 2024-11-11T11:58:37Z file_id: '56978' file_name: Biehler_INDRUM2020_283-287.pdf file_size: 576039 relation: main_file success: 1 file_date_updated: 2024-11-11T11:58:37Z has_accepted_license: '1' keyword: - Number Theory - Algebra - Discrete Mathematics - Logic - Research in University Mathematics Edcuation language: - iso: eng main_file_link: - url: ⟨hal-03114041⟩ page: 283-287 place: Bizerte, Tunisia publication: 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 related_material: link: - relation: confirmation url: https://hal.science/hal-03114041/ status: public title: University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic type: book_chapter user_id: '37888' year: '2020' ... --- _id: '34841' abstract: - lang: eng 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" author: - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners - first_name: Raphael full_name: Müller, Raphael last_name: Müller 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 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} }' 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. short: J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322. date_created: 2022-12-22T10:50:03Z date_updated: 2025-06-13T08:18:30Z department: - _id: '102' doi: 10.1016/j.jnt.2019.11.007 external_id: arxiv: - '1904.02573 ' intvolume: ' 212' keyword: - Algebra and Number Theory language: - iso: eng page: 311-322 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier BV status: public title: The conductor density of local function fields with abelian Galois group type: journal_article user_id: '82981' volume: 212 year: '2020' ... --- _id: '34917' abstract: - lang: eng 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). author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer - first_name: Gabriele full_name: Nebe, Gabriele last_name: Nebe citation: 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 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} }' 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.' 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. short: M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325. date_created: 2022-12-23T11:05:09Z date_updated: 2023-12-06T10:05:59Z department: - _id: '102' doi: 10.1142/s1793042119500131 intvolume: ' 15' issue: '02' keyword: - Algebra and Number Theory language: - iso: eng page: 309-325 publication: International Journal of Number Theory publication_identifier: issn: - 1793-0421 - 1793-7310 publication_status: published publisher: World Scientific Pub Co Pte Lt status: public title: Quaternary quadratic lattices over number fields type: journal_article user_id: '82258' volume: 15 year: '2019' ... --- _id: '34916' 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. author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer citation: 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 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 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.' 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. short: M. Kirschmer, Journal of Number Theory 197 (2019) 121–134. date_created: 2022-12-23T11:04:34Z date_updated: 2023-12-06T10:07:17Z department: - _id: '102' doi: 10.1016/j.jnt.2018.08.004 intvolume: ' 197' keyword: - Algebra and Number Theory language: - iso: eng page: 121-134 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier BV status: public title: Automorphisms of even unimodular lattices over number fields type: journal_article user_id: '82258' volume: 197 year: '2019' ... --- _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." author: - first_name: Andreas-Stephan full_name: Elsenhans, Andreas-Stephan last_name: Elsenhans - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners citation: 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 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 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} }' 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.' 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. short: A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20. date_created: 2022-12-22T10:52:18Z date_updated: 2023-03-06T09:05:51Z department: - _id: '102' doi: 10.1016/j.jsc.2018.04.013 external_id: arxiv: - '1610.06837 ' intvolume: ' 93' keyword: - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 1-20 publication: Journal of Symbolic Computation publication_identifier: issn: - 0747-7171 publication_status: published publisher: Elsevier BV status: public title: Computing subfields of number fields and applications to Galois group computations type: journal_article user_id: '93826' volume: 93 year: '2018' ... --- _id: '42790' 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. author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer citation: 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 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} }' 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.' 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.' 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. date_created: 2023-03-07T08:27:36Z date_updated: 2023-04-04T09:07:32Z department: - _id: '102' doi: 10.5802/jtnb.1052 extern: '1' intvolume: ' 30' issue: '3' keyword: - Algebra and Number Theory language: - iso: eng page: 847-857 publication: Journal de Théorie des Nombres de Bordeaux publication_identifier: issn: - 1246-7405 - 2118-8572 publication_status: published publisher: Cellule MathDoc/CEDRAM status: public title: One-class genera of exceptional groups over number fields type: journal_article user_id: '93826' volume: 30 year: '2018' ... --- _id: '1590' 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." author: - first_name: Michael full_name: Lass, Michael id: '24135' last_name: Lass orcid: 0000-0002-5708-7632 - first_name: Stephan full_name: Mohr, Stephan last_name: Mohr - first_name: Hendrik full_name: Wiebeler, Hendrik last_name: Wiebeler - first_name: Thomas full_name: Kühne, Thomas id: '49079' last_name: Kühne - first_name: Christian full_name: Plessl, Christian id: '16153' last_name: Plessl orcid: 0000-0001-5728-9982 citation: 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 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} }' 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.' 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.' 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.' conference: end_date: 2018-07-04 location: Basel, Switzerland name: Platform for Advanced Scientific Computing Conference (PASC) start_date: 2018-07-02 date_created: 2018-03-22T10:53:01Z date_updated: 2023-09-26T11:48:12Z department: - _id: '27' - _id: '518' - _id: '304' doi: 10.1145/3218176.3218231 external_id: arxiv: - '1710.10899' keyword: - approximate computing - linear algebra - matrix inversion - matrix p-th roots - numeric algorithm - parallel computing language: - iso: eng place: New York, NY, USA project: - _id: '32' grant_number: PL 595/2-1 / 320898746 name: Performance and Efficiency in HPC with Custom Computing - _id: '52' name: Computing Resources Provided by the Paderborn Center for Parallel Computing publication: Proc. Platform for Advanced Scientific Computing (PASC) Conference publication_identifier: isbn: - 978-1-4503-5891-0/18/07 publisher: ACM quality_controlled: '1' status: public title: A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices type: conference user_id: '15278' year: '2018' ... --- _id: '42791' abstract: - lang: eng 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. author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer - first_name: Marion G. full_name: Rüther, Marion G. last_name: Rüther 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 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 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} }' 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.' 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.' 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. short: M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548. date_created: 2023-03-07T08:28:11Z date_updated: 2023-04-04T09:10:14Z department: - _id: '102' doi: 10.1016/j.jalgebra.2017.02.029 extern: '1' intvolume: ' 480' keyword: - Algebra and Number Theory language: - iso: eng page: 519-548 publication: Journal of Algebra publication_identifier: issn: - 0021-8693 publication_status: published publisher: Elsevier BV status: public title: The constructive membership problem for discrete two-generator subgroups of SL(2,R) type: journal_article user_id: '93826' volume: 480 year: '2017' ... --- _id: '34844' 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. ' author: - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners - first_name: Florin full_name: Nicolae, Florin last_name: Nicolae citation: 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 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 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} }' 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.' 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.' 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. date_created: 2022-12-22T10:52:47Z date_updated: 2023-03-06T10:44:22Z department: - _id: '102' doi: 10.1016/j.jnt.2016.03.023 external_id: arxiv: - '1509.06883 ' intvolume: ' 167' keyword: - Algebra and Number Theory language: - iso: eng page: 161-168 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier BV status: public title: Are number fields determined by Artin L-functions? type: journal_article user_id: '93826' volume: 167 year: '2016' ... --- _id: '42792' abstract: - lang: eng 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. author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer - first_name: David full_name: Lorch, David last_name: Lorch 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 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} }' 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. short: M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361. date_created: 2023-03-07T08:28:46Z date_updated: 2023-04-04T09:10:42Z department: - _id: '102' doi: 10.1016/j.jnt.2014.11.001 extern: '1' intvolume: ' 161' keyword: - Algebra and Number Theory language: - iso: eng page: 343-361 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier BV status: public title: Ternary quadratic forms over number fields with small class number type: journal_article user_id: '93826' volume: 161 year: '2016' ... --- _id: '42793' abstract: - lang: eng 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. author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer citation: 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 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} }' 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.' 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.' 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. short: M. Kirschmer, Journal of Number Theory 136 (2014) 375–393. date_created: 2023-03-07T08:29:34Z date_updated: 2023-04-04T09:13:29Z department: - _id: '102' doi: 10.1016/j.jnt.2013.10.007 extern: '1' intvolume: ' 136' keyword: - Algebra and Number Theory language: - iso: eng page: 375-393 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier BV status: public title: One-class genera of maximal integral quadratic forms type: journal_article user_id: '93826' volume: 136 year: '2014' ... --- _id: '37672' 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. author: - first_name: Margit full_name: Rösler, Margit id: '37390' last_name: Rösler - first_name: Tom full_name: Koornwinder, Tom last_name: Koornwinder - first_name: Michael full_name: Voit, Michael last_name: Voit citation: 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 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} }' 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.' 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.' 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. date_created: 2023-01-20T09:37:16Z date_updated: 2023-01-24T22:15:13Z department: - _id: '555' doi: 10.1112/s0010437x13007045 intvolume: ' 149' issue: '8' keyword: - Algebra and Number Theory language: - iso: eng page: 1381-1400 publication: Compositio Mathematica publication_identifier: issn: - 0010-437X - 1570-5846 publication_status: published publisher: Wiley status: public title: Limit transition between hypergeometric functions of type BC and type A type: journal_article user_id: '93826' volume: 149 year: '2013' ... --- _id: '42797' 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. ' author: - first_name: Markus full_name: Kirschmer, Markus id: '82258' last_name: Kirschmer citation: 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 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} }' 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.' 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. short: M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634. date_created: 2023-03-07T08:35:56Z date_updated: 2023-04-04T09:22:22Z department: - _id: '102' doi: 10.1090/s0025-5718-2011-02570-6 extern: '1' intvolume: ' 81' issue: '279' keyword: - Applied Mathematics - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 1619-1634 publication: Mathematics of Computation publication_identifier: issn: - 0025-5718 - 1088-6842 publication_status: published publisher: American Mathematical Society (AMS) status: public title: A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$ type: journal_article user_id: '93826' volume: 81 year: '2012' ...