Remarks on the mixed joint universality for a class of zeta-functions

TL;DR

This paper discusses advanced properties of certain zeta-functions, including their functional independence and a generalized universality, extending the understanding of their complex behaviors in number theory.

Contribution

It introduces new insights into mixed joint universality and functional independence for polynomial Euler products and periodic Hurwitz zeta-functions with transcendental parameters.

Findings

Establishment of mixed joint functional independence.

Development of a generalized universality encompassing multiple periodic Hurwitz zeta-functions.

Insights into the complex behaviors of these zeta-functions.

Abstract

Two remarks related with the mixed joint universality for a polynomial Euler product and a periodic Hurwitz zeta-function with a transcendental parameter are given. One is the mixed joint functional independence, and the other is a generalized universality, which includes several periodic Hurwitz zeta-functions.