The discrete universality of the periodic Hurwitz zeta function

Abstract

The periodic Hurwitz zeta function , s=σ+it, 0<α≤1, is defined, for σ>1, by and by analytic continuation elsewhere. Here {a m } is a periodic sequence of complex numbers. In this paper, a discrete universality theorem for the function with a transcendental parameter α is proved. Roughly speaking, this means that every analytic function can be approximated uniformly on compact sets by shifts , where m is a non-negative integer and h is a fixed positive number such that is rational.