Communications in Number Theory and Physics

Volume 7 (2013)

Number 3

Asymptotic formulas for coefficients of inverse theta functions

Pages: 497 – 513



Kathrin Bringmann (Mathematical Institute, University of Cologne, Germany)

Jan Manschot (Camille Jordan Institute, University of Lyon, Villeurbanne, France)


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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