Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2026
|
| Soggetti: | |
| Accesso online: | https://doi.org/10.5281/zenodo.19456664 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901778536071168 |
|---|---|
| author | Alex Shvets |
| author_facet | Alex Shvets |
| contents | <p>We prove A(pm) ≡ A(m) (mod p⁴) for all primes p ≥ 5 and all m ≥ 1, where A_n = 27^n [z^n] ₂F₁(1/3,1/3;1;z)³. The proof combines a Hecke descent from level 3p to level 3, a Fricke–Hecke intertwining lemma giving a cusp-zero filtration, and a weakly holomorphic basis on X₀(3). No case-by-case computation is needed; the argument is uniform in p. Supplementary scripts provide independent verification for all primes up to 499.</p> <p><a href="https://arxiv.org/abs/2604.06238">https://arxiv.org/abs/2604.06238</a></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19456664 |
| 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 CM point Apéry-like sequence Dwork conjecture supercongruence eta quotient modular form order drop hypergeometric function Hecke descent Beukers factorization Lagrange-Bürmann Eisenstein series coupled cancellation <p>We prove A(pm) ≡ A(m) (mod p⁴) for all primes p ≥ 5 and all m ≥ 1, where A_n = 27^n [z^n] ₂F₁(1/3,1/3;1;z)³. The proof combines a Hecke descent from level 3p to level 3, a Fricke–Hecke intertwining lemma giving a cusp-zero filtration, and a weakly holomorphic basis on X₀(3). No case-by-case computation is needed; the argument is uniform in p. Supplementary scripts provide independent verification for all primes up to 499.</p> <p><a href="https://arxiv.org/abs/2604.06238">https://arxiv.org/abs/2604.06238</a></p> |
| title | Order drop, Hecke descent, and an unconditional mod p⁴ supercongruence for Sym³ hypergeometric coefficients |
| topic | symmetric cube Mao-Tian recurrence CM point Apéry-like sequence Dwork conjecture supercongruence eta quotient modular form order drop hypergeometric function Hecke descent Beukers factorization Lagrange-Bürmann Eisenstein series coupled cancellation |
| url | https://doi.org/10.5281/zenodo.19456664 |