The modified Mellin transform of powers of the zeta-function
Abstract
Description
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 $k = 1,2$.
20 pages
20 pages