A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS

Shekhar . Suman; Raman Kumar Das

doi:10.56827/JRSMMS.2022.1001.8

A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS

Shekhar . Suman Department of Mathematics, Ranchi University, Ranchi, Jharkhand, INDIA
Raman Kumar Das Department of Mathematics, St. Xavier’s College, Ranchi, Jharkhand, INDIA

DOI: https://doi.org/10.56827/JRSMMS.2022.1001.8

Keywords: Riemann zeta function, Riemann xi function, Riemann Hypothesis, Hadamard product.

Abstract

In this manuscript we denote by P ρ 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

Published

2022-12-30

Issue

Vol 10 No 01 (2022): J. of Ramanujan Society of Mathematics and Mathematical Sciences

Section

Research Article

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