On the estimation of some Mellin transforms connected with the fourth moment of $|\zeta (1/2+it)|$

Abstract

Mean square estimates for $Z_2(s)={\int }_1^{\infty }|\zeta (1/2+ix){|}^4{x}^{-s}dx(\Re s>1)$ are discussed, and some related Mellin transforms of quantities connected with the fourth power moment of $|\zeta (1/2+ix){|}^4$.

14 pages