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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 Li's criterion ： ウィキペディア英語版 Li's criterion In number theory, Li's criterion is a particular statement about the positivity of a certain sequence that is completely equivalent to the Riemann hypothesis. The criterion is named after Xian-Jin Li, who presented it in 1997. Recently, Enrico Bombieri and Jeffrey C. Lagarias provided a generalization, showing that Li's positivity condition applies to any collection of points that lie on the Re ''s'' = 1/2 axis. ==Definition== The Riemann ξ function is given by :$\backslash xi\; (s)=\backslash fracs(s-1)\; \backslash pi^\; \backslash Gamma\; \backslash left(\backslash frac\backslash right)\; \backslash zeta(s)$ where ζ is the Riemann zeta function. Consider the sequence :$\backslash lambda\_n\; =\; \backslash frac\; \backslash left.\; \backslash frac$ \left(\log \xi(s) \right ) \right|_. Li's criterion is then the statement that :''the Riemann hypothesis is completely equivalent to the statement that $\backslash lambda\_n\; >\; 0$ for every positive integer ''n''.'' The numbers $\backslash lambda\_n$ may also be expressed in terms of the non-trivial zeros of the Riemann zeta function: :$\backslash lambda\_n=\backslash sum\_\; \backslash left($ \left(1-\frac\right)^n\right ) where the sum extends over ρ, the non-trivial zeros of the zeta function. This conditionally convergent sum should be understood in the sense that is usually used in number theory, namely, that :$\backslash sum\_\backslash rho\; =\; \backslash lim\_\; \backslash sum\_.$ 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「Li's criterion」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.