정수계수 이차형식

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

• 밀그램의 정리
• 스미스-민코프스키-지겔 질량 공식
• 격자의 세타함수

계산 리소스

• A Catalogue of Lattices

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.