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Some identities for the Riemann zeta-function

Aleksandar Ivic
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Abstract

Several identities for the Riemann zeta-function $ζ(s)$ are proved. For example, if $s = σ+ it$ and $σ> 0$, then $$ \int_{-\infty}^\infty |{(1-2^{1-s})ζ(s)\over s}|^2dt = {π\overσ}(1 - 2^{1-2σ})ζ(2σ). $$

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Aleksandar Ivic. 2003-11-06. Some identities for the Riemann zeta-function. https://arxiv.org/abs/math/0305219

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