Hecke Relations for Eta Multipliers and Congruences of Higher-Order Smallest Parts Functions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913257616310272 |
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| author | Williams, Clayton |
| author_facet | Williams, Clayton |
| contents | We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, yielding congruences for their coefficients modulo powers of primes. As an application we derive systematic congruences for several higher-order smallest parts functions modulo prime powers, resolving a question of Garvan for these cases. We also relate moments of cranks and ranks to the partition function modulo prime powers. Some of our results strengthen and generalize those of a 2023 paper by Wang and Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hecke Relations for Eta Multipliers and Congruences of Higher-Order Smallest Parts Functions Williams, Clayton Number Theory 11F37 (Primary) 11F33, 11P83 (Secondary) We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, yielding congruences for their coefficients modulo powers of primes. As an application we derive systematic congruences for several higher-order smallest parts functions modulo prime powers, resolving a question of Garvan for these cases. We also relate moments of cranks and ranks to the partition function modulo prime powers. Some of our results strengthen and generalize those of a 2023 paper by Wang and Yang. |
| title | Hecke Relations for Eta Multipliers and Congruences of Higher-Order Smallest Parts Functions |
| topic | Number Theory 11F37 (Primary) 11F33, 11P83 (Secondary) |
| url | https://arxiv.org/abs/2403.04909 |