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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.22607 |
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| _version_ | 1866912608989216768 |
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| author | Diamantis, Nikolaos Pimm, Joshua |
| author_facet | Diamantis, Nikolaos Pimm, Joshua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Summation Formulas for Harmonic Maass Forms Diamantis, Nikolaos Pimm, Joshua Number Theory 11N37, 11F37, 11P84 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. |
| title | Summation Formulas for Harmonic Maass Forms |
| topic | Number Theory 11N37, 11F37, 11P84 |
| url | https://arxiv.org/abs/2509.22607 |