Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910926367621120 |
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| author | Garvan, Frank Morrow, Connor |
| author_facet | Garvan, Frank Morrow, Connor |
| contents | We prove multiplicative congruences mod $2^{12}$ for George Andrews's partition function, $\overline{\mathcal{EO}}(n)$, the number of partitions of $n$ in which every even part is less than each odd part and only the largest even part occurs an odd number of times. We find analogous congruences for more general infinite products. These congruences are obtained using Fricke involutions and Newman's approach to half integer weight Hecke operators on eta quotients, and were inspired by Atkin's multiplicative congruences for the partition function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01344 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products Garvan, Frank Morrow, Connor Number Theory Combinatorics Primary 11P82, Secondary 05A30, 11P83, 11F25, 11F37 We prove multiplicative congruences mod $2^{12}$ for George Andrews's partition function, $\overline{\mathcal{EO}}(n)$, the number of partitions of $n$ in which every even part is less than each odd part and only the largest even part occurs an odd number of times. We find analogous congruences for more general infinite products. These congruences are obtained using Fricke involutions and Newman's approach to half integer weight Hecke operators on eta quotients, and were inspired by Atkin's multiplicative congruences for the partition function. |
| title | Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products |
| topic | Number Theory Combinatorics Primary 11P82, Secondary 05A30, 11P83, 11F25, 11F37 |
| url | https://arxiv.org/abs/2505.01344 |