Riesz Means of Quadratic Class Numbers

Olivia Beckwith; Tushar Karmakar

Riesz Means of Quadratic Class Numbers

Number Theory 2026-06-27 v1

Authors: Olivia Beckwith , Tushar Karmakar

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, Imamo\={g}lu, and T\'{o}th.

Keywords

Riesz means class numbers Maass forms mock modular forms L-functions

Cite

@article{arxiv.2606.28657,
  title  = {Riesz Means of Quadratic Class Numbers},
  author = {Olivia Beckwith and Tushar Karmakar},
  journal= {arXiv preprint arXiv:2606.28657},
  year   = {2026}
}