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Pythagoras0 (토론 | 기여) (새 문서: ==개요== * 정수계수 이변수 이차형식(binary integral quadratic forms) * 정수계수 삼변수 이차형식(ternary integral quadratic forms) ==주요 정리== *...) |
Pythagoras0 (토론 | 기여) |
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| (같은 사용자의 중간 판 13개는 보이지 않습니다) | |||
| 2번째 줄: | 2번째 줄: | ||
* [[정수계수 이변수 이차형식(binary integral quadratic forms)]] | * [[정수계수 이변수 이차형식(binary integral quadratic forms)]] | ||
* [[정수계수 삼변수 이차형식(ternary integral quadratic forms)]] | * [[정수계수 삼변수 이차형식(ternary integral quadratic forms)]] | ||
| + | * [[16차원 짝수 자기쌍대 격자]] | ||
| + | * [[24차원 짝수 자기쌍대 격자]] | ||
==주요 정리== | ==주요 정리== | ||
* [[밀그램의 정리]] | * [[밀그램의 정리]] | ||
| + | * [[스미스-민코프스키-지겔 질량 공식]] | ||
| + | * [[격자의 세타함수]] | ||
| + | |||
| + | ==계산 리소스== | ||
| + | * [http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/ A Catalogue of Lattices] | ||
| + | |||
| + | |||
| + | ==리뷰, 에세이, 강의노트== | ||
| + | * Rudolf Scharlau, 2007, [http://www.mathematik.tu-dortmund.de/~scharlau/research/talks/scharlau-qfc2007.pdf Martin Kneser’s Work on Quadratic Forms and Algebraic Groups] | ||
| + | * Nebe, [http://www.math.rwth-aachen.de/~Gabriele.Nebe/talks/lat1op.pdf Lattices and modular forms] | ||
| + | * Hoehn, Gerald. 2002. “Genera of Vertex Operator Algebras and Three Dimensional Topological Quantum Field Theories.” arXiv:math/0209333, September. http://arxiv.org/abs/math/0209333. | ||
| + | * Nikulin, V. V. 1980. “Integral symmetric bilinear forms and some of their applications.” Mathematics of the USSR-Izvestiya 14 (1): 103. doi:10.1070/IM1980v014n01ABEH001060. | ||
| + | |||
| + | |||
| + | ==관련논문== | ||
| + | * Sardari, Naser Talebizadeh. “Optimal Strong Approximation for Quadratic Forms.” arXiv:1510.00462 [math], October 1, 2015. http://arxiv.org/abs/1510.00462. | ||
| + | * http://arxiv.org/abs/1509.04757 | ||
| + | * Nguyen, Phong Q., and Igor E. Shparlinski. ‘Counting Co-Cyclic Lattices’. arXiv:1505.06429 [cs, Math], 24 May 2015. http://arxiv.org/abs/1505.06429. | ||
| + | * Chan, Wai Kiu, and James Ricci. ‘The Representation of Integers by Positive Ternary Quadratic Polynomials’. arXiv:1505.00281 [math], 1 May 2015. http://arxiv.org/abs/1505.00281. | ||
| + | * Bhargava, M., J. E. Cremona, T. A. Fisher, N. G. Jones, and J. P. Keating. ‘What Is the Probability That a Random Integral Quadratic Form in <math>n</math> Variables Has an Integral Zero?’. arXiv:1502.05992 [math], 20 February 2015. http://arxiv.org/abs/1502.05992. | ||
| + | * Nebe, Gabriele. “Automorphisms of Extremal Unimodular Lattices in Dimension 72.” arXiv:1409.8473 [math], September 30, 2014. http://arxiv.org/abs/1409.8473. | ||
[[분류:정수론]] | [[분류:정수론]] | ||
2020년 11월 16일 (월) 04:20 기준 최신판
개요
- 정수계수 이변수 이차형식(binary integral quadratic forms)
- 정수계수 삼변수 이차형식(ternary integral quadratic forms)
- 16차원 짝수 자기쌍대 격자
- 24차원 짝수 자기쌍대 격자
주요 정리
계산 리소스
리뷰, 에세이, 강의노트
- Rudolf Scharlau, 2007, Martin Kneser’s Work on Quadratic Forms and Algebraic Groups
- Nebe, Lattices and modular forms
- Hoehn, Gerald. 2002. “Genera of Vertex Operator Algebras and Three Dimensional Topological Quantum Field Theories.” arXiv:math/0209333, September. http://arxiv.org/abs/math/0209333.
- Nikulin, V. V. 1980. “Integral symmetric bilinear forms and some of their applications.” Mathematics of the USSR-Izvestiya 14 (1): 103. doi:10.1070/IM1980v014n01ABEH001060.
관련논문
- Sardari, Naser Talebizadeh. “Optimal Strong Approximation for Quadratic Forms.” arXiv:1510.00462 [math], October 1, 2015. http://arxiv.org/abs/1510.00462.
- http://arxiv.org/abs/1509.04757
- Nguyen, Phong Q., and Igor E. Shparlinski. ‘Counting Co-Cyclic Lattices’. arXiv:1505.06429 [cs, Math], 24 May 2015. http://arxiv.org/abs/1505.06429.
- Chan, Wai Kiu, and James Ricci. ‘The Representation of Integers by Positive Ternary Quadratic Polynomials’. arXiv:1505.00281 [math], 1 May 2015. http://arxiv.org/abs/1505.00281.
- Bhargava, M., J. E. Cremona, T. A. Fisher, N. G. Jones, and J. P. Keating. ‘What Is the Probability That a Random Integral Quadratic Form in \(n\) Variables Has an Integral Zero?’. arXiv:1502.05992 [math], 20 February 2015. http://arxiv.org/abs/1502.05992.
- Nebe, Gabriele. “Automorphisms of Extremal Unimodular Lattices in Dimension 72.” arXiv:1409.8473 [math], September 30, 2014. http://arxiv.org/abs/1409.8473.