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21 Publications
2022 | Preprint | LibreCat-ID: 43392
Kirschmer, Markus, and Jürgen Klüners. “Chow Groups of Orders in Number Fields,” 2022.
LibreCat
2022 | Journal Article | LibreCat-ID: 45854
Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number Fields.” Experimental Mathematics 31, no. 1 (2022): 280–301. https://doi.org/10.1080/10586458.2019.1618756.
LibreCat
| DOI
2021 | Journal Article | LibreCat-ID: 34912
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.
LibreCat
| DOI
2019 | Journal Article | LibreCat-ID: 34915
Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” Archiv Der Mathematik 113, no. 4 (2019): 337–47. https://doi.org/10.1007/s00013-019-01348-z.
LibreCat
| DOI
2019 | Journal Article | LibreCat-ID: 34917
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.
LibreCat
| DOI
2019 | Journal Article | LibreCat-ID: 34916
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.
LibreCat
| DOI
2018 | Book Chapter | LibreCat-ID: 42788
Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-70566-8_22.
LibreCat
| DOI
2018 | Journal Article | LibreCat-ID: 42790
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.
LibreCat
| DOI
2017 | Journal Article | LibreCat-ID: 42791
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.
LibreCat
| DOI
2016 | Journal Article | LibreCat-ID: 42792
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.
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| DOI
2016 | Misc | LibreCat-ID: 43454
Kirschmer, Markus. Definite Quadratic and Hermitian Forms with Small Class Number (Habilitation). RWTH Aachen University, 2016.
LibreCat
2014 | Journal Article | LibreCat-ID: 42793
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.
LibreCat
| DOI
2014 | Journal Article | LibreCat-ID: 42801
Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of the Modular Group .” Glasgow Mathematical Journal 57, no. 1 (2014): 173–80. https://doi.org/10.1017/s0017089514000202.
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| DOI
2014 | Journal Article | LibreCat-ID: 42794
Eick, B., Markus Kirschmer, and C. Leedham-Green. “The Constructive Membership Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” LMS Journal of Computation and Mathematics 17, no. 1 (2014): 345–59. https://doi.org/10.1112/s1461157014000047.
LibreCat
| DOI
2013 | Book Chapter | LibreCat-ID: 42805
Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” In Integers. DE GRUYTER, 2013. https://doi.org/10.1515/9783110298161.212.
LibreCat
| DOI
2013 | Journal Article | LibreCat-ID: 42796
Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” LMS Journal of Computation and Mathematics 16 (2013): 172–86. https://doi.org/10.1112/s1461157013000107.
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| DOI
2012 | Journal Article | LibreCat-ID: 42797
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.
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| DOI
2011 | Journal Article | LibreCat-ID: 42798
Kirschmer, Markus. “Finite Symplectic Matrix Groups.” Experimental Mathematics 20, no. 2 (2011): 217–28. https://doi.org/10.1080/10586458.2011.564964.
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| DOI
2010 | Journal Article | LibreCat-ID: 42803
Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” SIAM Journal on Computing 39, no. 5 (2010): 1714–47. https://doi.org/10.1137/080734467.
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| DOI
2009 | Dissertation | LibreCat-ID: 43453
Kirschmer, Markus. Finite Symplectic Matrix Groups (Dissertation). RWTH Aachen University, 2009.
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