Order drop, Hecke descent, and an unconditional mod p⁴ supercongruence for Sym³ hypergeometric coefficients
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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Zenodo
2026
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| _version_ | 1866901795568091136 |
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| author | Alex Shvets |
| author_facet | Alex Shvets |
| contents | <p>We prove a supercongruence modulo p to the fourth for the coefficients of the symmetric cube of the hypergeometric function at parameters one third, one third, one. The proof combines a modular identification on X_0(3), an Eisenstein-type congruence for the coefficients of the Hauptmodul derivative, Lagrange–Bürmann coefficient extraction, and a Fricke–Hecke descent argument that yields uniform vanishing of all defects.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19648644 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Order drop, Hecke descent, and an unconditional mod p⁴ supercongruence for Sym³ hypergeometric coefficients Alex Shvets symmetric cube Mao-Tian recurrence Apéry-like sequence supercongruence eta quotient modular form order drop hypergeometric function Hecke descent Lagrange-Bürmann Eisenstein series arithmetic specialization Dwork-type congruence <p>We prove a supercongruence modulo p to the fourth for the coefficients of the symmetric cube of the hypergeometric function at parameters one third, one third, one. The proof combines a modular identification on X_0(3), an Eisenstein-type congruence for the coefficients of the Hauptmodul derivative, Lagrange–Bürmann coefficient extraction, and a Fricke–Hecke descent argument that yields uniform vanishing of all defects.</p> |
| title | Order drop, Hecke descent, and an unconditional mod p⁴ supercongruence for Sym³ hypergeometric coefficients |
| topic | symmetric cube Mao-Tian recurrence Apéry-like sequence supercongruence eta quotient modular form order drop hypergeometric function Hecke descent Lagrange-Bürmann Eisenstein series arithmetic specialization Dwork-type congruence |
| url | https://doi.org/10.5281/zenodo.19648644 |