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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 Witten zeta function ： ウィキペディア英語版 Witten zeta function In mathematics, the Witten zeta function, introduced by , is a function associated to a root system that encodes the degrees of the irreducible representations of the corresponding Lie group. It is a special case of the Shintani zeta function. ==Definition== Witten's original definition of the zeta function of a semisimple Lie group was :$\backslash sum\_R\backslash frac$ where the sum is over equivalence classes of irreducible representations ''R''. If Δ of rank ''r'' is a root system with ''n'' positive roots in Δ+ and with simple roots λ''i'', the Witten zeta function of several variables is given by :$\backslash zeta\_W(s\_1,\backslash dots,s\_n)\; =\; \backslash sum\_\backslash prod\_\backslash frac\{(\backslash alpha^\backslash or,\; m\_1\backslash lambda\_1+\backslash cdots+m\_r\backslash lambda\_r)^\{s\_\backslash alpha\}\},$ The original zeta function studied by Witten differed from this slightly, in that all the numbers ''s''α are equal, and the function is multiplied by a constant. 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「Witten zeta 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.