An identity concerning the Riemann-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.

7 pages. arXiv admin note: text overlap with arXiv:2012.09091