Effective hybrid joint universality for Dirichlet $L$-functions and its application

TL;DR

This paper extends the hybrid joint universality theorem to Dirichlet L-functions with prime moduli and applies these results to estimate the density of universality for Hurwitz zeta-functions with rational parameters.

Contribution

It generalizes the universality lower bounds for Dirichlet L-functions and applies these to Hurwitz zeta-functions, advancing understanding of their universality properties.

Findings

Lower bounds for the density of universality for Dirichlet L-functions.

Application of these bounds to Hurwitz zeta-functions.

Extension of universality results to functions with rational parameters.

Abstract

In 2003, Garunk\v{s}tis provided a lower bound for the lower density of the universality theorem for the Riemann zeta-function. In this paper, we generalize this result for the hybrid joint universality theorem for Dirichlet $L$-functions whose moduli are prime numbers. Furthermore, by its application, we estimate a lower bound of the lower density of the universality theorem for Hurwitz zeta-functions with rational parameters.