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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 Mangoldt function ： ウィキペディア英語版 Von Mangoldt function In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither multiplicative nor additive. ==Definition== The von Mangoldt function, denoted by , is defined as : The values of for the first nine positive numbers are :$0\; ,\; \backslash log\; 2\; ,\; \backslash log\; 3\; ,\; \backslash log\; 2\; ,\; \backslash log\; 5\; ,\; 0\; ,\; \backslash log\; 7\; ,\; \backslash log\; 2\; ,\; \backslash log\; 3,$ which is related to . The summatory von Mangoldt function, , also known as the Chebyshev function, is defined as :$\backslash psi(x)\; =\; \backslash sum\_\; \backslash Lambda(n).$ von Mangoldt provided a rigorous proof of an explicit formula for involving a sum over the non-trivial zeros of the Riemann zeta function. This was an important part of the first proof of the prime number theorem. 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「Von Mangoldt 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.