The modified Mellin transform of powers of the zeta-function

Aleksandar Ivić

The modified Mellin transform of powers of the zeta-function

Number Theory 2007-05-23 v1

Authors: Aleksandar Ivić

Abstract

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

Keywords

modified Mellin transform zeta-function analytic continuation mean square estimates power moments

Cite

@article{arxiv.math/0502011,
  title  = {The modified Mellin transform of powers of the zeta-function},
  author = {Aleksandar Ivić},
  journal= {arXiv preprint arXiv:math/0502011},
  year   = {2007}
}

Comments

20 pages

Related papers

View all related →