지겔 모듈라 형식

지겔 상반 공간

• 지겔 상반 공간 $\mathcal{H}_g$

$$ \mathcal{H}_g=\left\{\tau \in M_{g \times g}(\mathbb{C}) \ \big| \ \tau^{\mathrm{T}}=\tau, \textrm{Im}(\tau) \text{ positive definite} \right\} $$

• 사교군 $\Gamma_g:={\rm Sp}(g,\Z)$
• $\mathcal{A}_g=\mathcal{H}_g/\Gamma_g$ : moduli space of principally polarized abelian varieties

지겔 모듈라 형식의 예

• 격자의 지겔 세타 급수

관련된 항목들

• 리만 곡면의 주기 행렬과 겹선형 관계 (bilinear relation)
• 사교 행렬
• 16차원 짝수 자기쌍대 격자
• 24차원 짝수 자기쌍대 격자

계산 리소스

• Siegel modular forms in SAGE

사전 형태의 자료

• http://en.wikipedia.org/wiki/Siegel_modular_form

리뷰, 에세이, 강의노트

• Kohnen, A short course on Siegel modular forms
• Van der Geer, Gerard. 2006. “Siegel Modular Forms.” arXiv:math/0605346 (May 12). http://arxiv.org/abs/math/0605346.
• Chiera, Some aspects of the theory of theta series
• Ghitza, 2004, An elementary introduction to Siegel modular forms

관련논문

• Vinberg, E. 2013. “On the Algebra of Siegel Modular Forms of Genus 2.” Transactions of the Moscow Mathematical Society 74: 1–13. doi:10.1090/S0077-1554-2014-00217-X.
• Katsurada, Hidenori. "An explicit formula for Siegel series." American journal of mathematics (1999): 415-452.
• Katsurada, Hidenori. "An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree $3$." Nagoya Mathematical Journal 146 (1997): 199-223.
• Tsuyumine, Shigeaki. “Thetanullwerte on a Moduli Space of Curves and Hyperelliptic Loci.” Mathematische Zeitschrift 207, no. 1 (May 1, 1991): 539–68. doi:10.1007/BF02571407.

관련도서

• Andrianov, Anatoli. Introduction to Siegel Modular Forms and Dirichlet Series Springer, 2010.
• Klingen, Helmut. Introductory Lectures on Siegel Modular Forms. Cambridge University Press, 1990.
• Maass, Lectures on Siegel's Modular Functions