# Mixed Rademacher and BPS Black Holes

## TL;DR

This paper derives an exact asymptotic expansion for the Fourier coefficients of mixed mock Jacobi forms counting 1/4-BPS states in Type IIB string theory, linking number theory with black hole entropy calculations.

## Contribution

It refines the Hardy-Ramanujan-Littlewood circle method to handle mixed mock Jacobi forms and compares the results with supergravity entropy computations.

## Key findings

- Derived an exact asymptotic expansion for Fourier coefficients of mixed mock Jacobi forms.
- Validated the expansion by comparing with supergravity entropy calculations.
- Enhanced understanding of BPS state degeneracies in string theory.

## Abstract

Dyonic 1/4-BPS states in Type IIB string theory compactified on $\mathrm{K}3 \times T^2$ are counted by meromorphic Jacobi forms. The finite parts of these functions, which are mixed mock Jacobi forms, account for the degeneracy of states stable throughout the moduli space of the compactification. In this paper, we obtain an exact asymptotic expansion for their Fourier coefficients, refining the Hardy-Ramanujan-Littlewood circle method to deal with their mixed-mock character. The result is compared to a low-energy supergravity computation of the exact entropy of extremal dyonic 1/4-BPS single-centered black holes, obtained by applying supersymmetric localization techniques to the quantum entropy function.