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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 Selberg's zeta function conjecture ： ウィキペディア英語版 Selberg's zeta function conjecture In mathematics, the Selberg conjecture, named after Atle Selberg, is about the density of zeros of the Riemann zeta function ζ(1/2 + ''it''). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. Results on this can be formulated in terms of ''N''(''T''), the function counting zeroes on the line for which the value of ''t'' satisfies 0 ≤ ''t'' ≤ ''T''. ==Background== In 1942 Atle Selberg investigated the problem of the Hardy–Littlewood conjecture 2; and he proved that for any :$\backslash varepsilon\; >\; 0$ there exist :$T\_0\; =\; T\_0(\backslash varepsilon)\; >\; 0$ and :$c\; =\; c(\backslash varepsilon)\; >\; 0,$ such that for :$T\; \backslash geq\; T\_0$ and :$H=T^$ the inequality :$N(T+H)-N(T)\; \backslash geq\; cH\backslash log\; T$ holds true. In his turn, Selberg stated a conjecture relating to shorter intervals, namely that it is possible to decrease the value of the exponent ''a'' = 0.5 in :$H=T^.$ 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「Selberg's zeta function conjecture」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.