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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 Vinogradov's theorem ： ウィキペディア英語版 Vinogradov's theorem In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers. It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a representation for all odd integers greater than five. It is named after Ivan Matveyevich Vinogradov who proved it in the 1930s. Hardy and Littlewood had shown earlier that this result followed from the generalized Riemann hypothesis, and Vinogradov was able to remove this assumption. The full statement of Vinogradov's theorem gives asymptotic bounds on the number of representations of an odd integer as a sum of three primes. ==Statement of Vinogradov's theorem== Let ''A'' be a positive real number. Then :$r(N)=G(N)N^2+O\backslash left(N^2\backslash log^N\backslash right),$ where :$r(N)=\backslash sum\_\backslash Lambda(k\_1)\backslash Lambda(k\_2)\backslash Lambda(k\_3),$ using the von Mangoldt function $\backslash Lambda$, and :$G(N)=\backslash left(\backslash prod\_\backslash left(1-\backslash right)\backslash right)\backslash left(\backslash prod\_\backslash left(1+\backslash right)\backslash right).$ 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「Vinogradov'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.