Asymptotic formulas for coefficients of inverse theta functions

2013/04/26 by Bringmann, Kathrin, Manschot, Jan
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1304.7208

Abstract

We determine asymptotic formulas for the coefficients of a natural class of negative index and negative weight Jacobi forms. These coefficients can be viewed as a refinement of the numbers p_k(n) of partitions of n into k colors. Part of the motivation for this work is that they are equal to the Betti numbers of the Hilbert scheme of points on an algebraic surface S and appear also as counts of Bogomolny-Prasad-Sommerfield (BPS) states in physics.

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