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arXiv · 2509.22607

Summation Formulas for Harmonic Maass Forms

Nikolaos Diamantis·Joshua Pimm
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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 $L$-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.

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Nikolaos Diamantis, Joshua Pimm. 2025-09-26. Summation Formulas for Harmonic Maass Forms. https://arxiv.org/abs/2509.22607

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