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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 Zeta function universality ： ウィキペディア英語版 Zeta function universality In mathematics, the universality of zeta-functions is the remarkable ability of the Riemann zeta-function and other, similar, functions, such as the Dirichlet L-functions, to approximate arbitrary non-vanishing holomorphic functions arbitrarily well. The universality of the Riemann zeta function was first proven by Sergei Mikhailovitch Voronin in 1975〔Voronin, S.M. (1975) "Theorem on the Universality of the Riemann Zeta Function." Izv. Akad. Nauk SSSR, Ser. Matem. 39 pp.475-486. Reprinted in Math. USSR Izv. 9, 443-445, 1975〕 and is sometimes known as Voronin's Universality Theorem. ==Formal statement== A mathematically precise statement of universality for the Riemann zeta-function ζ(''s'') follows. Let ''U'' be a compact subset of the strip : such that the complement of ''U'' is connected. Let be a continuous function on ''U'' which is holomorphic on the interior of ''U'' and does not have any zeros in ''U''. Then for any there exists a such that : Even more: the lower density of the set of values ''t'' which do the job is positive, as is expressed by the following inequality about a limit inferior. : \liminf_ \frac \,\lambda\!\left( \left\ \right) , where ''λ'' denotes the Lebesgue measure on the real numbers. 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「Zeta function universality」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.