Abstract

The microstate degeneracies of quarter BPS dyons in N=4 string theory are encoded in a meromorphic Siegel modular form. I will describe how one can obtain an expression for the single-centered black hole degeneracies as an infinite sum over the residues of the Siegel modular form. The final expression is a generalised Rademacher expansion which coincides with and unifies the previous known results. The starting point takes the form of a sum over saddles, thus providing predictions for the localisation of the gravitational path integral for quarter BPS black holes. During the talk I will highlight the appearance of different number theoretic structures such as mock modular forms, shadows and continued fractions, and how they can arise from the supergravity localisation computation. This is based on joint works with Gabriel Cardoso, Abhiram Kidambi, Suresh Nampuri and Valentin Reys.