翻訳と辞書 Words near each other ・ Character literal ・ Character Map ・ Character map ・ Character mask ・ Character Of Generation ・ Character of Robert E. Howard ・ Character of the Happy Warrior ・ Character orientation ・ Character piece ・ Character race ・ Character sheet ・ Character sketch ・ Character Strengths and Virtues ・ Character structure ・ Character Studio ・ Character sum ・ Character table ・ Character Technical Director ・ Character theory ・ Character theory (media) ・ Character variety ・ Character-count integrity ・ Character-oriented terminal ・ Characterisation (law) ・ Characterisation of pore space in soil ・ Characteristic ・ Characteristic (algebra) ・ Characteristic 2 type ・ Characteristic admittance ・ Characteristic based product configurator Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Character sum ： ウィキペディア英語版 Character sum In mathematics, a character sum is a sum :$\backslash Sigma\; \backslash chi(n)\backslash ,$ of values of a Dirichlet character χ ''modulo'' ''N'', taken over a given range of values of ''n''. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue ''modulo'' ''N''. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform). Assume χ is a nonprincipal Dirichlet character to the modulus ''N''. ==Sums over ranges== The sum taken over all residue classes mod ''N'' is then zero. This means that the cases of interest will be sums $\backslash Sigma$ over relatively short ranges, of length ''R'' < ''N'' say, : A fundamental improvement on the trivial estimate $\backslash Sigma\; =\; O(N)$ is the Pólya–Vinogradov inequality (George Pólya, I. M. Vinogradov, independently in 1918), stating in big O notation that :$\backslash Sigma\; =\; O(\backslash sqrt\backslash log\; N).$ Assuming the generalized Riemann hypothesis, Hugh Montgomery and R. C. Vaughan have shown〔Montgomery and Vaughan (1977)〕 that there is the further improvement :$\backslash Sigma\; =\; O(\backslash sqrt\backslash log\backslash log\; N).$ 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「Character 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.