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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 Liouville's function ： ウィキペディア英語版 Liouville function The Liouville function, denoted by λ(''n'') and named after Joseph Liouville, is an important function in number theory. If ''n'' is a positive integer, then λ(''n'') is defined as: :$\backslash lambda(n)\; =\; (-1)^,\backslash ,\backslash !$ where Ω(''n'') is the number of prime factors of ''n'', counted with multiplicity . λ is completely multiplicative since Ω(''n'') is completely additive, i.e.: Ω(''ab'') = Ω(''a'') + Ω(''b''). The number one has no prime factors, so Ω(1) = 0 and therefore λ(1) = 1. The Liouville function satisfies the identity: :$$ \sum_\lambda(d) = \begin 1 & \textn\text \\ 0 & \text \end The Liouville function's Dirichlet inverse is the absolute value of the Möbius function. ==Series== The Dirichlet series for the Liouville function is related to the Riemann zeta function by :$\backslash frac\; =\; \backslash sum\_^\backslash infty\; \backslash frac.$ The Lambert series for the Liouville function is :$\backslash sum\_^\backslash infty\; \backslash frac\; =$ \sum_^\infty q^ = \frac\left(\vartheta_3(q)-1\right), where $\backslash vartheta\_3(q)$ is the Jacobi theta function. 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「Liouville 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.