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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 Erdős–Kac theorem ： ウィキペディア英語版 Erdős–Kac theorem In number theory, the Erdős–Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory, states that if ω(''n'') is the number of distinct prime factors of ''n'', then, loosely speaking, the probability distribution of : $\backslash frac$. ==Precise statement== For any fixed ''a'' < ''b'', :$\backslash lim\_\; \backslash left\; (\; \backslash frac\; \backslash cdot\; \backslash \#\backslash left\backslash \}\; \backslash le\; b\; \backslash right\backslash \}\; \backslash right\; )\; =\; \backslash Phi(a,b)$ where $\backslash Phi(a,b)$ is the normal (or "Gaussian") distribution, defined as : $\backslash Phi(a,b)=\; \backslash frac\; \backslash ,\; dt.$ More generally, if f(''n'') is a strongly additive function ($\backslash scriptstyle\; f(p\_1^\backslash cdots\; p\_k^)=f(p\_1)+\backslash cdots+f(p\_k)$) with $\backslash scriptstyle\; |f(p)|\backslash le1$ for all prime ''p'', then :$\backslash lim\_\; \backslash left\; (\; \backslash frac\; \backslash cdot\; \backslash \#\backslash left\backslash \; \backslash le\; b\; \backslash right\backslash \}\; \backslash right\; )\; =\; \backslash Phi(a,b)$ with :$A(n)=\backslash sum\_\backslash frac,\backslash qquad\; B(n)=\backslash sqrt\}.$ 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「Erdős–Kac 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.