A note on series equivalent of the Riemann hypothesis

被引：0
|
作者：
Suman, Shekhar [1 ]
Das, Raman Kumar [2 ]
机构：
[1] Ranchi Univ, Dept Math, Ranchi, Bihar, India
[2] St Xaviers Coll, Dept Math, Ranchi, Bihar, India
来源：
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2023年 / 54卷 / 01期
关键词：
Riemann zeta function; Riemann xi function; Ricmann Hypothesis; Hadamard product;
D O I：
10.1007/s13226-022-00237-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this manuscript we denote by Sigma(rho) a sum over the non trivial zeros of Riemann zeta function (or over the zeros of Riemann's xi function), where the zeros of multiplicity k are counted k times. We prove a result that the Riemann Hypothesis is true if and only if Sigma(rho) 1/vertical bar 1/2 - rho vertical bar(2 )= xi '' (1/2) / xi(1/2)
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页码：117 / 119
页数：3
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