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arXiv · 1304.7208

Asymptotic formulas for coefficients of inverse theta functions

Kathrin Bringmann·Jan Manschot
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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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Kathrin Bringmann, Jan Manschot. 2013-04-26. Asymptotic formulas for coefficients of inverse theta functions. https://arxiv.org/abs/1304.7208

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