Zero Attractors of Partition Polynomials

TL;DR

This paper investigates the zeros of partition polynomials, revealing their asymptotic behavior and the influence of the oot dilogarithm on their zero distribution within the unit disk.

Contribution

It introduces a detailed analysis of the zeros of partition polynomials and connects their asymptotics to the properties of the oot dilogarithm, a novel approach in this area.

Findings

Zeros form a network of curves inside the unit disk

Asymptotics determine the zero distribution behavior

The oot dilogarithm plays a key role in the analysis

Abstract

A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics determine the limiting behavior of their zeros which form a network of curves inside the unit disk. An important new feature in their study requires a detailed analysis of. the \root dilogarithm" given as the real part of the square root of the usual dilogarithm.