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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 Weber's modular function ： ウィキペディア英語版 Weber modular function In mathematics, the Weber modular functions are a family of three modular functions ''f'', ''f''1, and ''f''2, studied by Heinrich Martin Weber. ==Definition== Let $q\; =\; e^$ where ''τ'' is an element of the upper half-plane. :$\backslash begin$ \mathfrak(\tau) &= q^}\prod_(1+q^}) = e^}\frac\big)}=\frac\big)\eta(2\tau)}\\ \mathfrak_1(\tau) &= q^}\prod_(1-q^}) = \frac\big)}\\ \mathfrak_2(\tau) &= \sqrt2\, q^}\prod_(1+q^)= \frac \end where$\backslash eta(\backslash tau)$ is the Dedekind eta function. Note the eta quotients immediately imply that, :$\backslash mathfrak(\backslash tau)\backslash mathfrak\_1(\backslash tau)\backslash mathfrak\_2(\backslash tau)\; =\backslash sqrt$ The transformation ''τ'' → –1/''τ'' fixes ''f'' and exchanges ''f''1 and ''f''2. So the 3-dimensional complex vector space with basis ''f'', ''f''1 and ''f''2 is acted on by the group SL2(Z). 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「Weber modular function」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.