Zero Attractors of Partition Polynomials

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.