The Mellin transform of the square of Riemann's zeta-function

Aleksandar Ivić

The Mellin transform of the square of Riemann's zeta-function

Number Theory 2007-05-23 v2

Authors: Aleksandar Ivić

Abstract

Let ${\cal Z}_1(s) = \int_1^\infty |\zeta({1\over2}+ix)|^2x^{-s}{\rm d}x (\sigma = \Re s > 1)$ . A result concerning analytic continuation of ${\cal Z}_1(s)$ to $\bf C$ is proved, and also a result relating the order of ${\cal Z}_1(\sigma + it) (1/2 \le \sigma \le 1, t\ge t_0)$ to the order of ${\cal Z}_1({1\over2}+it)$ .

Keywords

mellin transform riemann zeta-function analytic continuation order of functions square of zeta-function

Cite

@article{arxiv.math/0411040,
  title  = {The Mellin transform of the square of Riemann's zeta-function},
  author = {Aleksandar Ivić},
  journal= {arXiv preprint arXiv:math/0411040},
  year   = {2007}
}

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9 pages

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