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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 Gross–Koblitz formula ： ウィキペディア英語版 Gross–Koblitz formula In mathematics, the Gross–Koblitz formula, introduced by expresses a Gauss sum using a product of values of the p-adic gamma function. It is an analog of the Chowla–Selberg formula for the usual gamma function. It implies the Hasse–Davenport relation and generalizes the Stickelberger theorem. gave another proof of the Gross–Koblitz formula using Dwork's work, and gave an elementary proof. ==Statement== The Gross–Koblitz formula states that the Gauss sum τ can be given in terms of the ''p''-adic gamma function Γ''p'' by :$\backslash tau\_q(r)\; =\; -\backslash pi^\backslash prod\_\backslash Gamma\_p(r^/(q-1))$ where * ''q'' is a power ''p''''f'' of a prime ''p'' *''r'' is an integer with 0 ≤ r < q–1 * ''r''(i) is the integer whose base ''p'' expansion is a cyclic permutation of the ''f'' digits of ''r'' by ''i'' positions. * ''s''''p''(''r'') is the sum of the digits of ''r'' in base ''p'' $\backslash tau\_q(r)\; =\; \backslash sum\_a^\backslash zeta\_\backslash pi^$ where the sum is over roots of 1 in the extension Q''p''(π) *π satisfies π''p'' – 1 = –''p'' *ζπ is the ''p''th root of 1 congruent to 1+π mod π2 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「Gross–Koblitz formula」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.