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Riemann假设一个等价命题的证明

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Riemann假设一个等价命题的证明 

Proof of an Equivalent Proposition of Riemann Hypothesis

发布时间:2016-12-19  浏览量:30  收藏数:0  评论数:0

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朱玉扬*
(  合肥学院数学与物理系;  )
摘要: 运用Chebyshev函数与素数定理等证明:存在正常数A,对所有自然数n≥A,那么有 exp(Hn)log(Hn)—σ(n)﹥eγnloglogn—σ(n)﹥0. 这里σ(n)是自然数n的所有因子和,Hn是1到n的所有自然数的倒数之和。由Robin定理,Riemann假设被证明成立。
关键词: Riemann 假设;非平凡零点;调和数;不等式; 素数
Zhu Yuyang*
(  Department of mathematics, Hefei University;  )
Abstract: Using Chebyshev function and prime number theorem, this paper proves that, there exists a positive constant A, such that for all natural numbers n≥A, exp(Hn)log(Hn)-σ(n)﹥eγnloglogn-σ(n)﹥0. According to Robin theorem, the Riemann Hypothesis is proved. Where Hn is the reciprocal sum of all natural numbers from 1 to n.
Keywords: Riemann hypothesis; non-trivial zeros; harmonic number; inequality; prime number

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作者简介: Zhu Yuyang, male, Professor of mathematics and physics, Hefei University, research direction: number theory and combinatorics.
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