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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 Real analytic Eisenstein series ： ウィキペディア英語版 Real analytic Eisenstein series In mathematics, the simplest real analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL(2,R) and in analytic number theory. It is closely related to the Epstein zeta function. There are many generalizations associated to more complicated groups. ==Definition== The Eisenstein series ''E''(''z'', ''s'') for ''z'' = ''x'' + ''iy'' in the upper half-plane is defined by :$E(z,s)\; =\backslash sum\_\{y^s\backslash over|mz+n|^\{2s\}\}$ for Re(''s'') > 1, and by analytic continuation for other values of the complex number ''s''. The sum is over all pairs of coprime integers. Warning: there are several other slightly different definitions. Some authors omit the factor of ½, and some sum over all pairs of integers that are not both zero; which changes the function by a factor of ζ(2''s''). 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「Real analytic Eisenstein series」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.