Joint discrete universality for periodic zeta-functions

Abstract

In the paper, joint universality theorems for periodic zeta functions with multiplicative coefficients and periodic Hurwitz zeta-functions are proved. The main theorem of [11] is extended, and two new joint universality theorems on the approximation of a collection of analytic functions by discrete shifts of the above zeta- functions are obtained. For this, certain linear independence hypotheses are applied.

Mathematics Subject Classification (2010): Primary 11M41; Secondary 41A30.

Keywords: Mergelyan theorem, periodic Hurwitz zeta-function, periodic zeta-function, universality, Voronin theorem