On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider approximation of analytic functions discrete shifts function, and prove that, for arbitrary parameters step arithmetic progression, there closed non-empty subset space in critical strip such that its can be approximated function. set those infinite, it has positive density. For proof, weak convergence probability measures applied.