Study on a Riemann Hypothesis related Inequality
首发时间:2015-12-10
Abstract:According to Robin's theorem, the necessary and sufficient condition of Riemann hypothesis being true is for arbitrarily natural number n≥A,such that exp(Hn)log(Hn) - ∑d|n d ≥ 0. Here A is a positive constant, Hn=1+1/2+1/3+…+(1/n). Using mathematical analysis, Chebyshev function and the equivalence property of prime number theorem we give that limn-?∞{exp(Hn)log(Hn)- ∑d|n d} ≥ 0. So limn-?∞inf{exp(Hn)log(Hn)- ∑d|n d} ≥ 0.
keywords: Number theory Riemann hypothesis non-trivial zeros harmonic number inequality prime number.
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Riemann假设一个相关不等式的研究
摘要:利用Robin定理指出, Riemann假设成立的充要条件是: Hn=1+1/2+1/3+…+(1/n), 存在正常数A,对所有自然数n≥A,有exp(Hn)log(Hn)- ∑d|n d ≥ 0.运用分析的方法以及Chebyshev函数与素数定理的等价性质证明limn-?∞{exp(Hn)log(Hn)- ∑d|n d} ≥ 0.由此得到limn-?∞inf{exp(Hn)log(Hn)- ∑d|n d} ≥ 0.
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