Hybrid subconvexity and the partition function

Abstract

We give an upper bound for the error term in the Hardy-Ramanujan-Rademacher formula for the partition function. The main input is a new hybrid subconvexity bound for the central value $L(\frac{1}{2},f\times (\frac{q}{\cdot }))$ in the $q$ and spectral parameter aspects, where $f$ is a Hecke-Maass cusp form for $\hat{I}{“}_0(N)$ and $q$ is a fundamental discriminant.

19 pages