The modified Mellin transform of powers of the zeta-function

Aleksandar Ivić

The modified Mellin transform ${\mathcal{Z}}_k(s)={\int }_1^{\infty }|\zeta (1/2+ix){|}^{2k}{x}^{-s}\mathrm{d}x(k=1,2,...)$ is investigated. Analytic continuation and mean square estimates of ${\c…