On the Discrete Approximation by the Mellin Transform of the Riemann Zeta-Function

Abstract

In the paper, it is obtained that there are infinite discrete shifts Ξ(s+ikh), h>0, k∈N0 of the Mellin transform Ξ(s) of the square of the Riemann zeta-function, approximating a certain class of analytic functions. For the proof, a probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied.