Modularity of moments of reciprocal sums for partitions into distinct parts
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909573912199168 |
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| author | Bringmann, Kathrin Kim, Byungchan Kim, Eunmi |
| author_facet | Bringmann, Kathrin Kim, Byungchan Kim, Eunmi |
| contents | In this paper, we determine modularity properties of the generating function of $s_k(n)$ which sums $k$-th power of reciprocals of parts throughout all of the partitions of $n$ into distinct parts. In particular, we show that the generating function for $s_k (n)$ is related to Maass Eisenstein series and sesquiharmonic Maass forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modularity of moments of reciprocal sums for partitions into distinct parts Bringmann, Kathrin Kim, Byungchan Kim, Eunmi Number Theory 11F20, 11P82, 11P83 In this paper, we determine modularity properties of the generating function of $s_k(n)$ which sums $k$-th power of reciprocals of parts throughout all of the partitions of $n$ into distinct parts. In particular, we show that the generating function for $s_k (n)$ is related to Maass Eisenstein series and sesquiharmonic Maass forms. |
| title | Modularity of moments of reciprocal sums for partitions into distinct parts |
| topic | Number Theory 11F20, 11P82, 11P83 |
| url | https://arxiv.org/abs/2504.07644 |