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arXiv · 2101.01265

An identity concerning the Riemann-zeta function

Douglas Azevedo
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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.

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Douglas Azevedo. 2021-01-04. An identity concerning the Riemann-zeta function. https://arxiv.org/abs/2101.01265

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