Discrete universality for Matsumoto zeta-functions and the nontrivial zeros of the Riemann zeta-function

TL;DR

This paper extends the discrete universality theorem, previously proven for the Riemann zeta-function, to Matsumoto zeta-functions, highlighting the broad applicability of universality properties in complex analysis.

Contribution

It generalizes the discrete universality theorem to Matsumoto zeta-functions, expanding the scope of universality results beyond classical zeta-functions.

Findings

Discrete universality holds for Matsumoto zeta-functions.

Extension of universality from Riemann zeta to Matsumoto zeta-functions.

Broadens understanding of universality in zeta and L-functions.

Abstract

In 2017, Garunk\v{s}tis, Laurin\v{c}ikas and Macaitien\.{e} proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended in various zeta-functions and $L$-functions. In this paper, we generalize this discrete universality for Matsumoto zeta-functions.