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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 Igusa zeta function ： ウィキペディア英語版 Igusa zeta-function In mathematics, an Igusa zeta function is a type of generating function, counting the number of solutions of an equation, ''modulo'' ''p'', ''p''2, ''p''3, and so on. == Definition == For a prime number ''p'' let ''K'' be a p-adic field, i.e. , ''R'' the valuation ring and ''P'' the maximal ideal. For $z\; \backslash in\; K$ $\backslash operatorname(z)$ denotes the valuation of ''z'', $\backslash mid\; z\; \backslash mid\; =\; q^$, and $ac(z)=z\; \backslash pi^$ for a uniformizing parameter π of ''R''. Furthermore let $\backslash phi\; :\; K^n\; \backslash mapsto\; \backslash mathbb$ be a Schwartz–Bruhat function, i.e. a locally constant function with compact support and let $\backslash chi$ be a character of $K$ *. In this situation one associates to a non-constant polynomial $f(x\_1,\; \backslash ldots,\; x\_n)\; \backslash in\; K()$ the Igusa zeta function : $Z\_\backslash phi(s,\backslash chi)\; =\; \backslash int\_\; \backslash phi(x\_1,\backslash ldots,x\_n)\; \backslash chi(ac(f(x\_1,\backslash ldots,x\_n)))\; |f(x\_1,\backslash ldots,x\_n)|^s\; \backslash ,\; dx$ where $s\; \backslash in\; \backslash mathbb,\; \backslash operatorname(s)>0,$ and ''dx'' is Haar measure so normalized that $R^n$ has measure 1. 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「Igusa 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.