Riesz Means of Quadratic Class Numbers

Abstract

We prove an asymptotic formula for a weighted Riesz mean of Hurwitz class numbers and real quadratic class numbers. To do this, we introduce L-functions for weight $\frac {1}{2} $ sesquiharmonic Maass forms of moderate growth and prove a formula for the Riesz means of the corresponding generalized mock modular forms, generalizing a recent result of the first author with Diamantis, Gupta, Rolen, and Thalagoda for mock modular forms. We then apply this formula to a sesquiharmonic Maass form that was first introduced by Duke, Imamoglu, and Tóth.