On certain class of entire functions and a conjecture by Alan Sokal

TL;DR

This paper characterizes a specific class of entire functions based on their odd and even parts, revealing unique zero localization properties, and applies these findings to address a case of Alan Sokal's conjecture.

Contribution

It introduces a new class of entire functions with distinctive zero distribution properties and applies these to a specific case of Sokal's conjecture.

Findings

Zeros of the class are localized in a unique way

The class is characterized by conditions on odd and even parts

A particular case of Sokal's conjecture is resolved

Abstract

In this paper we determine a class of entire functions using conditions on their odd and even parts. Further it is shown that the zeros of members of this class are localized in a very special way. This result allows us to treat a particular case of a conjecture by A. Sokal.