# On mixed joint discrete universality for a class of zeta-functions III

## TL;DR

This paper establishes the most general results to date on the discrete mixed joint value-distribution and universality properties of Matsumoto and periodic Hurwitz zeta-functions under linear independence conditions.

## Contribution

It provides the broadest known conditions under which discrete mixed joint universality holds for these classes of zeta-functions.

## Key findings

- Most general results on discrete mixed joint universality
- Conditions involving linear independence of parameters
- Applicability to Matsumoto and periodic Hurwitz zeta-functions

## Abstract

We present the most general at this moment results on the discrete mixed joint value-distribution and the universality property for the class of Matsumoto zeta-functions and periodic Hurwitz zeta-functions under certain linear independence condition on the relevant parameters, such as common differences of arithmetic progressions, prime numbers etc.