On mixed joint discrete universality for a class of zeta-functions: One more case

TL;DR

This paper establishes a new case of mixed discrete joint universality for certain zeta-functions, demonstrating their approximation capabilities under specific rational and transcendental conditions.

Contribution

It extends previous universality results to the original class of Matsumoto and periodic Hurwitz zeta-functions with new rational and transcendental parameter conditions.

Findings

Proves a new mixed discrete joint universality theorem

Shows approximation of target functions by shifts of zeta-functions

Works with original zeta-functions, not partial sums

Abstract

We prove a new case of mixed discrete joint universality theorem on approximation of certain target couple of analytic functions by the shifts of a pair consisting of the function belonging to wide class of Matsumoto zeta-functions and the periodic Hurwitz zeta-function. We work under the condition that the common difference of arithmetical progression satisfies a certain rational condition and the parameter is a transcendental number. The essential difference from the result in our previous article is that here we do not study the class of partial zeta-functions, but work with the class of the original functions.