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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 Landau's function ： ウィキペディア英語版 Landau's function In mathematics, Landau's function ''g''(''n''), named after Edmund Landau, is defined for every natural number ''n'' to be the largest order of an element of the symmetric group ''S''''n''. Equivalently, ''g''(''n'') is the largest least common multiple (lcm) of any partition of ''n'', or the maximum number of times a permutation of ''n'' elements can be recursively applied to itself before it returns to its starting sequence. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so ''g''(5) = 6. An element of order 6 in the group ''S''5 can be written in cycle notation as (1 2) (3 4 5). The integer sequence ''g''(0) = 1, ''g''(1) = 1, ''g''(2) = 2, ''g''(3) = 3, ''g''(4) = 4, ''g''(5) = 6, ''g''(6) = 6, ''g''(7) = 12, ''g''(8) = 15, ... is named after Edmund Landau, who proved in 1902〔Landau, pp. 92–103〕 that :$\backslash lim\_\backslash frac.$ The statement that : for all sufficiently large ''n'', where Li−1 denotes the inverse of the logarithmic integral function, is equivalent to the Riemann hypothesis. It can be shown that : and indeed :$g(n)\; \backslash le\; \backslash exp\backslash left(1.05314\backslash sqrt\backslash right).$〔Jean-Pierre Massias, Majoration explicite de l'ordre maximum d'un élément du groupe symétrique, ''Ann. Fac. Sci. Toulouse Math.'' (5) 6 (1984), no. 3-4, pp. 269–281 (1985).〕 ==Notes== 〔 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「Landau's function」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.