Improved asymptotics for moments of reciprocal sums for partitions into distinct parts
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910725775032320 |
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| author | Bringmann, Kathrin Kim, Byungchan Kim, Eunmi |
| author_facet | Bringmann, Kathrin Kim, Byungchan Kim, Eunmi |
| contents | In this paper we strongly improve asymptotics for $s_1(n)$ (respectively $s_2(n)$) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of $n$ into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not posses product expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved asymptotics for moments of reciprocal sums for partitions into distinct parts Bringmann, Kathrin Kim, Byungchan Kim, Eunmi Number Theory 11F20, 11P82, 11P83 In this paper we strongly improve asymptotics for $s_1(n)$ (respectively $s_2(n)$) which sums reciprocals (respectively squares of reciprocals) of parts throughout all the partitions of $n$ into distinct parts. The methods required are much more involved than in the case of usual partitions since the generating functions are not modular and also do not posses product expansions. |
| title | Improved asymptotics for moments of reciprocal sums for partitions into distinct parts |
| topic | Number Theory 11F20, 11P82, 11P83 |
| url | https://arxiv.org/abs/2412.02534 |