An identity concerning the Riemann-zeta function

2021/01/04 by Douglas Azevedo, Azevedo, Douglas
Mathematics · #11M26 #11M41 #Advanced Mathematical Identities #Analytic Number Theory Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.01265

openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a certain function J(s) we prove that the identity (ζ(2s))/(ζ(s))-(s-(1)/(2))J(s)=(ζ(2s+1))/(ζ(s+1/2)), holds in the half-plane Re(s)>1/2 and both sides of the equality are analytic in this half-plane.

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