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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 Dirichlet density ： ウィキペディア英語版 Dirichlet density In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Peter Gustav Lejeune Dirichlet, is a measure of the size of the set that is easier to use than the natural density. ==Definition== If ''A'' is a subset of the prime numbers, the Dirichlet density of ''A'' is the limit :$\backslash lim\_\; \backslash frac\}\}$ if it exists. Note that since $\backslash sim\; \backslash log(\backslash frac)\}$ as $s\backslash rightarrow\; 1^+$ (see Prime zeta function), this is also equal to :$\backslash lim\_\backslash over\; \backslash log(\backslash frac)\}.$ This expression is usually the order of the "pole" of :$\backslash prod\_\{1\backslash over\; 1-p^\{-s\}\}$ at ''s'' = 1, (though in general it is not really a pole as it has non-integral order), at least if the function on the right is a holomorphic function times a (real) power of ''s''−1 near ''s'' = 1. For example, if ''A'' is the set of all primes, the function on the right is the Riemann zeta function which has a pole of order 1 at ''s'' = 1, so the set of all primes has Dirichlet density 1. More generally, one can define the Dirichlet density of a sequence of primes (or prime powers), possibly with repetitions, in the same way. 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「Dirichlet density」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.