An identity concerning the Riemann-zeta function

TL;DR

The paper proves a new identity involving the Riemann zeta function and a related function J(s), valid in the half-plane where the real part of s exceeds 1/2.

Contribution

It introduces and proves a novel identity connecting ratios of the Riemann zeta function and a specific auxiliary function J(s).

Findings

The identity holds in the half-plane Re(s)>1/2.

Both sides of the identity are analytic in this region.

The result provides new insights into the properties of the zeta function.

Abstract

For a certain function $J(s)$ we prove that the identity $$\frac{\zeta(2s)}{\zeta(s)}-\left(s-\frac{1}{2}\right)J(s)=\frac{\zeta(2s+1)}{\zeta(s+1/2)}, $$ holds in the half-plane Re$(s)>1/2$ and both sides of the equality are analytic in this half-plane.