On the zeros of generalized Hurwitz zeta functions

TL;DR

This paper proves the existence of infinitely many zeros of certain generalized Hurwitz zeta functions within their domain of absolute convergence, extending classical results about the Hurwitz zeta function.

Contribution

It generalizes classical zero results of the Hurwitz zeta function to a broader class of generalized Hurwitz zeta functions.

Findings

Infinitely many zeros exist in the domain of absolute convergence

Generalization of Davenport, Heilbronn, and Cassels' classical problem

Extension to a broader class of zeta functions

Abstract

In this note, we prove the existence of infinitely many zeros of certain generalized Hurwitz zeta functions in the domain of absolute convergence. This is a generalization of a classical problem of Davenport, Heilbronn and Cassels about the zeros of the Hurwitz zeta function.