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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 Rankin–Cohen bracket ： ウィキペディア英語版 Rankin–Cohen bracket In mathematics, the Rankin–Cohen bracket of two modular forms is another modular form, generalizing the product of two modular forms. gave some general conditions for polynomials in derivatives of modular forms to be modular forms, and found the explicit examples of such polynomials that give Rankin–Cohen brackets. They were named by , who introduced Rankin–Cohen algebras as an abstract setting for Rankin–Cohen brackets. ==Definition== If $f(\backslash tau)$ and $g(\backslash tau)$ are modular form of weight ''k'' and ''h'' respectively then their ''n''th Rankin–Cohen bracket ()''n'' is given by :$()\_n\; =\; \backslash sum\_\; (-1)^r\backslash binom\backslash binom\; \backslash frac\backslash frac\; \backslash \; .$ It is a modular form of weight ''k'' + ''h'' + 2''n''. Note that here the derivative operator here is normalized so that $\backslash frac=\backslash frac\; f\text{'}(\backslash tau)$ where $f\text{'}(\backslash tau)$ is the standard derivative. 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「Rankin–Cohen bracket」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.