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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 Chowla–Mordell theorem ： ウィキペディア英語版 Chowla–Mordell theorem In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. In detail, if $p$ is a prime number, $\backslash chi$ a nontrivial Dirichlet character modulo $p$, and :$G(\backslash chi)=\backslash sum\; \backslash chi(a)\; \backslash zeta^a$ where $\backslash zeta$ is a primitive $p$-th root of unity in the complex numbers, then :$\backslash frac$ is a root of unity if and only if $\backslash chi$ is the quadratic residue symbol modulo $p$. The 'if' part was known to Gauss: the contribution of Chowla and Mordell was the 'only if' direction. The ratio in the theorem occurs in the functional equation of L-functions. ==References== * ''Gauss and Jacobi Sums'' by Bruce C. Berndt, Ronald J. Evans and Kenneth S. Williams, Wiley-Interscience, p. 53. fi:Chowlan–Mordellin lause 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「Chowla–Mordell theorem」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.