Communications in Number Theory and Physics
Volume 7 (2013)
Asymptotic formulas for coefficients of inverse theta functions
Pages: 497 – 513
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.