On Zeros of Certain Entire Functions

TL;DR

This paper establishes a sufficient condition for genus 0 entire functions to have only negative zeros and explores implications for the Riemann hypothesis and its generalizations.

Contribution

It introduces a new criterion for zeros of certain entire functions and applies it to important problems in number theory.

Findings

Derived a sufficient condition for negative zeros of genus 0 entire functions

Applied the condition to the Riemann hypothesis and generalized Riemann hypothesis

Provided insights into the zero distribution of functions related to number theory

Abstract

Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive Dirichlet character.