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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 Quadratic Gauss sum ： ウィキペディア英語版 Quadratic Gauss sum In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws. == Definition == Let ''p'' be an odd prime number and ''a'' an integer. Then the Gauss sum mod ''p'', ''g''(''a'';''p''), is the following sum of the ''p''th roots of unity: : $g(a;p)\; =\backslash sum\_^e^=\backslash sum\_^\backslash zeta\_p^,$ \quad \zeta_p=e^. If ''a'' is not divisible by ''p'', an alternative expression for the Gauss sum (with the same value) is : $G(a,\backslash chi)=\backslash sum\_^\backslash left(\backslash frac\backslash right)e^.$ Here $\backslash chi(n)=\backslash left(\backslash frac\backslash right)$ is the Legendre symbol, which is a quadratic character mod ''p''. An analogous formula with a general character ''χ'' in place of the Legendre symbol defines the Gauss sum ''G''(''χ''). 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「Quadratic Gauss sum」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.