An infinite family of overpartition congruences mod powers of 2
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917036036194304 |
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| author | Shomanov, Zhumagali Garvan, Frank |
| author_facet | Shomanov, Zhumagali Garvan, Frank |
| contents | We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's $U_2$ operator, we determine lower bounds on the 2-adic valuations of the coefficients that arise at each step. Our approach yields new modular equations relating the Hauptmoduln $G_2$ on $Γ_0(2)$ and $G_8$ on $Γ_0(8)$, together with explicit $U_2$-action formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An infinite family of overpartition congruences mod powers of 2 Shomanov, Zhumagali Garvan, Frank Number Theory 11P83, 11F03 We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's $U_2$ operator, we determine lower bounds on the 2-adic valuations of the coefficients that arise at each step. Our approach yields new modular equations relating the Hauptmoduln $G_2$ on $Γ_0(2)$ and $G_8$ on $Γ_0(8)$, together with explicit $U_2$-action formulas. |
| title | An infinite family of overpartition congruences mod powers of 2 |
| topic | Number Theory 11P83, 11F03 |
| url | https://arxiv.org/abs/2510.20175 |