English

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 δ\delta-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}
}