Hyperbolicity of Appell Polynomials of Functions in the $\delta$-Laguerre-P\'olya Class
Number Theory
2020-02-25 v1
Abstract
We present a method for proving that Jensen polynomials associated with functions in the -Laguerre-P\'olya class have all real roots, and demonstrate how it can be used to construct new functions belonging to the Laguerre-P\'olya class. As an application, we confirm a conjecture of Ono, which asserts that the Jensen polynomials associated with the first term of the Hardy-Ramanujan-Rademacher series formula for the partition function are always hyperbolic.
Keywords
Cite
@article{arxiv.2002.09906,
title = {Hyperbolicity of Appell Polynomials of Functions in the $\delta$-Laguerre-P\'olya Class},
author = {Jonas Iskander and Vanshika Jain},
journal= {arXiv preprint arXiv:2002.09906},
year = {2020}
}