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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Siegel modular form ： ウィキペディア英語版 Siegel modular form In mathematics, Siegel modular forms are a major type of automorphic form. These stand in relation to the conventional ''elliptic'' modular forms as abelian varieties do in relation to elliptic curves; the complex manifolds constructed as in the theory are basic models for what a moduli space for abelian varieties (with some extra level structure) should be, as quotients of the Siegel upper half-space rather than the upper half-plane by discrete groups. The modular forms of the theory are holomorphic functions on the set of symmetric ''n'' × ''n'' matrices with positive definite imaginary part; the forms must satisfy an automorphy condition. Siegel modular forms can be thought of as multivariable modular forms, i.e. as special functions of several complex variables. Siegel modular forms were first investigated by Carl Ludwig Siegel in the 1930s for the purpose of studying quadratic forms analytically. These primarily arise in various branches of number theory, such as arithmetic geometry and elliptic cohomology. Siegel modular forms have also been used in some areas of physics, such as conformal field theory. ==Definition== ===Preliminaries=== Let $g,\; N\; \backslash in\; \backslash mathbb$ and define :$\backslash mathcal\_g=\backslash left\backslash )\; \backslash \; \backslash big|\; \backslash \; \backslash tau^(\backslash tau)\; \backslash text\; \backslash right\backslash \},$ the Siegel upper half-space. Define the symplectic group of level $N$, denoted by $\backslash Gamma\_g(N),$ as : where $I\_g$ is the $g\; \backslash times\; g$ identity matrix. Finally, let :$\backslash rho:\backslash textrm\_g(\backslash mathbb)\; \backslash rightarrow\; \backslash textrm(V)$ be a rational representation, where $V$ is a finite-dimensional complex vector space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Siegel modular form」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.