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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 Petersson inner product ： ウィキペディア英語版 Petersson inner product In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson. ==Definition== Let $\backslash mathbb\_k$ be the space of entire modular forms of weight $k$ and $\backslash mathbb\_k$ the space of cusp forms. The mapping $\backslash langle\; \backslash cdot\; ,\; \backslash cdot\; \backslash rangle\; :\; \backslash mathbb\_k\; \backslash times\; \backslash mathbb\_k\; \backslash rightarrow$ \mathbb, :$\backslash langle\; f\; ,\; g\; \backslash rangle\; :=\; \backslash int\_\backslash mathrm\; f(\backslash tau)\; \backslash overline$ (\operatorname\tau)^k d\nu (\tau) is called Petersson inner product, where :$\backslash mathrm\; =\; \backslash left\backslash \backslash tau\; \backslash right|\; \backslash leq\; \backslash frac,$ \left| \tau \right| \geq 1 \right\} is a fundamental region of the modular group $\backslash Gamma$ and for $\backslash tau\; =\; x\; +\; iy$ :$d\backslash nu(\backslash tau)\; =\; y^dxdy$ is the hyperbolic volume form. 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「Petersson inner product」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.