Summation Formulas for Harmonic Maass Forms
Number Theory
2025-09-29 v1
Abstract
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of -series of harmonic Maass forms to state and prove a summation formula for such forms without any restrictions on their growth. We deduce a summation formula for the partition function. We further employ the same theory to derive a result on classical modular forms, namely, a summation formula and the asymptotics of a Riesz sum attached to a cusp form.
Cite
@article{arxiv.2509.22607,
title = {Summation Formulas for Harmonic Maass Forms},
author = {Nikolaos Diamantis and Joshua Pimm},
journal= {arXiv preprint arXiv:2509.22607},
year = {2025}
}