[{"status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34840","intvolume":"        90","page":"1483-1497","citation":{"ieee":"J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class group of exponent $3$ and $5$,” <i>Mathematics of Computation</i>, vol. 90, no. 329, pp. 1483–1497, 2021, doi: <a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>.","chicago":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i> 90, no. 329 (2021): 1483–97. <a href=\"https://doi.org/10.1090/mcom/3609\">https://doi.org/10.1090/mcom/3609</a>.","ama":"Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>. 2021;90(329):1483-1497. doi:<a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>","bibtex":"@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}, volume={90}, DOI={<a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>}, 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 $5$.” <i>Mathematics of Computation</i>, vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:<a href=\"https://doi.org/10.1090/mcom/3609\">10.1090/mcom/3609</a>.","short":"J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.","apa":"Klüners, J., &#38; Komatsu, T. (2021). Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>, <i>90</i>(329), 1483–1497. <a href=\"https://doi.org/10.1090/mcom/3609\">https://doi.org/10.1090/mcom/3609</a>"},"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","doi":"10.1090/mcom/3609","volume":90,"author":[{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"},{"full_name":"Komatsu, Toru","last_name":"Komatsu","first_name":"Toru"}],"date_updated":"2023-03-06T08:57:45Z","abstract":[{"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. ","lang":"eng"}],"publication":"Mathematics of Computation","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"external_id":{"arxiv":["2004.03308v2"]},"year":"2021","issue":"329","title":"Imaginary multiquadratic number fields with class group of exponent $3$ and $5$","date_created":"2022-12-22T10:48:44Z","publisher":"American Mathematical Society (AMS)"},{"page":"401-449","intvolume":"        91","citation":{"apa":"Kirschmer, M., Narbonne, F., Ritzenthaler, C., &#38; Robert, D. (2021). Spanning the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>, <i>91</i>(333), 401–449. <a href=\"https://doi.org/10.1090/mcom/3672\">https://doi.org/10.1090/mcom/3672</a>","bibtex":"@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the isogeny class of a power of an elliptic curve}, volume={91}, DOI={<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>}, 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} }","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.” <i>Mathematics of Computation</i>, vol. 91, no. 333, American Mathematical Society (AMS), 2021, pp. 401–49, doi:<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>.","ieee":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the isogeny class of a power of an elliptic curve,” <i>Mathematics of Computation</i>, vol. 91, no. 333, pp. 401–449, 2021, doi: <a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>.","chicago":"Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” <i>Mathematics of Computation</i> 91, no. 333 (2021): 401–49. <a href=\"https://doi.org/10.1090/mcom/3672\">https://doi.org/10.1090/mcom/3672</a>.","ama":"Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>. 2021;91(333):401-449. doi:<a href=\"https://doi.org/10.1090/mcom/3672\">10.1090/mcom/3672</a>"},"year":"2021","issue":"333","publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","doi":"10.1090/mcom/3672","title":"Spanning the isogeny class of a power of an elliptic curve","volume":91,"date_created":"2022-12-23T11:02:02Z","author":[{"last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258","first_name":"Markus"},{"first_name":"Fabien","last_name":"Narbonne","full_name":"Narbonne, Fabien"},{"last_name":"Ritzenthaler","full_name":"Ritzenthaler, Christophe","first_name":"Christophe"},{"full_name":"Robert, Damien","last_name":"Robert","first_name":"Damien"}],"date_updated":"2023-04-04T07:52:43Z","publisher":"American Mathematical Society (AMS)","status":"public","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. "}],"publication":"Mathematics of Computation","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"department":[{"_id":"102"}],"user_id":"93826","_id":"34912"},{"user_id":"100441","department":[{"_id":"841"}],"_id":"45955","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"type":"journal_article","publication":"Mathematics of Computation","status":"public","author":[{"full_name":"Akrivis, Georgios","last_name":"Akrivis","first_name":"Georgios"},{"last_name":"Feischl","full_name":"Feischl, Michael","first_name":"Michael"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"first_name":"Christian","last_name":"Lubich","full_name":"Lubich, Christian"}],"date_created":"2023-07-10T11:42:57Z","volume":90,"publisher":"American Mathematical Society (AMS)","date_updated":"2024-04-03T09:20:36Z","doi":"10.1090/mcom/3597","title":"Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation","issue":"329","publication_status":"published","publication_identifier":{"issn":["0025-5718","1088-6842"]},"citation":{"short":"G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038.","mla":"Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i>, vol. 90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","bibtex":"@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90}, DOI={<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>}, 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} }","apa":"Akrivis, G., Feischl, M., Kovács, B., &#38; Lubich, C. (2020). Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>","ama":"Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>. 2020;90(329):995-1038. doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>","ieee":"G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation,” <i>Mathematics of Computation</i>, vol. 90, no. 329, pp. 995–1038, 2020, doi: <a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","chicago":"Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i> 90, no. 329 (2020): 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>."},"page":"995-1038","intvolume":"        90","year":"2020"},{"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","issue":"279","year":"2012","page":"1619-1634","intvolume":"        81","citation":{"bibtex":"@article{Kirschmer_2012, title={A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$}, volume={81}, DOI={<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>}, 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.","mla":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i>, vol. 81, no. 279, American Mathematical Society (AMS), 2012, pp. 1619–34, doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>.","apa":"Kirschmer, M. (2012). A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>, <i>81</i>(279), 1619–1634. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>","ieee":"M. Kirschmer, “A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$,” <i>Mathematics of Computation</i>, vol. 81, no. 279, pp. 1619–1634, 2012, doi: <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>.","chicago":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i> 81, no. 279 (2012): 1619–34. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>.","ama":"Kirschmer M. A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>. 2012;81(279):1619-1634. doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>"},"date_updated":"2023-04-04T09:22:22Z","publisher":"American Mathematical Society (AMS)","volume":81,"author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"date_created":"2023-03-07T08:35:56Z","title":"A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$","doi":"10.1090/s0025-5718-2011-02570-6","publication":"Mathematics of Computation","type":"journal_article","abstract":[{"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. ","lang":"eng"}],"status":"public","_id":"42797","department":[{"_id":"102"}],"user_id":"93826","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"extern":"1"},{"language":[{"iso":"eng"}],"abstract":[{"text":"Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for computing the lattice of subfields of L require the computation\r\nof all the conjugates of α. This is usually achieved by factoring the minimal\r\npolynomial mα(x) of α over L. In practice, the existing algorithms for factoring\r\npolynomials over algebraic number fields can handle only problems of moderate\r\nsize. In this paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm computes the Frobenius automorphism of p in time polynomial\r\nin the size of p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly chosen primes it is possible to compute all the conjugates of α.","lang":"eng"}],"publication":"Mathematics of Computation","title":"Computing Automorphisms of Abelian Number Fields","date_created":"2023-01-11T09:31:21Z","publisher":"American Mathematical Society (AMS)","year":"1999","issue":"227","user_id":"93826","department":[{"_id":"102"}],"_id":"35941","status":"public","type":"journal_article","author":[{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"},{"last_name":"Acciaro","full_name":"Acciaro, Vincenzo","first_name":"Vincenzo"}],"volume":68,"date_updated":"2023-03-06T10:28:52Z","citation":{"short":"J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.","bibtex":"@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro, Vincenzo}, year={1999}, pages={1179–1186} }","mla":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i>, vol. 68, no. 227, American Mathematical Society (AMS), 1999, pp. 1179–86.","apa":"Klüners, J., &#38; Acciaro, V. (1999). Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>, <i>68</i>(227), 1179–1186.","ieee":"J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,” <i>Mathematics of Computation</i>, vol. 68, no. 227, pp. 1179–1186, 1999.","chicago":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i> 68, no. 227 (1999): 1179–86.","ama":"Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>. 1999;68(227):1179-1186."},"page":"1179-1186","intvolume":"        68","related_material":{"link":[{"url":"https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf","relation":"confirmation"}]},"publication_status":"published","publication_identifier":{"issn":["1088-6842","0025-5718"]}}]