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The modified Mellin transform of powers of the zeta-function

Aleksandar Ivić
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Abstract

The modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty |ζ(1/2+ix)|^{2k}x^{-s}{\rm d} x (k = 1,2,...)$ is investigated. Analytic continuation and mean square estimates of ${\cal Z}_k(s) $ are discussed, as well as connections with power moments of $|ζ(1/2+ix)|$, with the special emphasis on the cases $k = 1,2$.

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Aleksandar Ivić. 2005-02-01. The modified Mellin transform of powers of the zeta-function. https://arxiv.org/abs/math/0502011

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