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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 Linnik's theorem ： ウィキペディア英語版 Linnik's theorem Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive ''c'' and ''L'' such that, if we denote ''p''(''a'',''d'') the least prime in the arithmetic progression :$a\; +\; nd,\backslash$ where ''n'' runs through the positive integers and ''a'' and ''d'' are any given positive coprime integers with 1 ≤ ''a'' ≤ ''d'' - 1, then: : The theorem is named after Yuri Vladimirovich Linnik, who proved it in 1944. Although Linnik's proof showed ''c'' and ''L'' to be effectively computable, he provided no numerical values for them. == Properties == It is known that ''L'' ≤ 2 for almost all integers ''d''. On the generalized Riemann hypothesis it can be shown that : $p(a,d)\; \backslash leq\; (1+o(1))\backslash varphi(d)^2\; \backslash ln^2\; d\; \backslash ;\; ,$ where $\backslash varphi$ is the totient function.〔 It is also conjectured that: : 〔 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「Linnik's theorem」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.