Hypergeometric supercongruences

DOI10.1007/978-3-030-04161-8_33zbMath1443.11022arXiv1803.10834OpenAlexW2795516613MaRDI QIDQ2001243

David P. Roberts, Fernando Rodriguez Villegas

Publication date: 2 July 2019

Full work available at URL: https://arxiv.org/abs/1803.10834

zbMATH Keywords

Hodge numbershypergeometric supercongruences

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Congruences for modular and (p)-adic modular forms (11F33) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (12)

A \(q\)-Dwork-type generalization of Rodriguez-Villegas' supercongruences ⋮ Special Hypergeometric Motives and Their L-Functions: Asai Recognition ⋮ A whipple \(_7F_6\) formula revisited ⋮ Some supercongruences of arbitrary length ⋮ A local-global theorem for \(p\)-adic supercongruences ⋮ A hypergeometric version of the modularity of rigid Calabi-Yau manifolds ⋮ Dwork-type supercongruences through a creative \(q\)-microscope ⋮ Congruences corresponding to hypergeometric identities. I: \(_2F_1\) transformations ⋮ Hypergeometric functions over finite fields ⋮ Some numeric hypergeometric supercongruences ⋮ Supercongruences for rigid hypergeometric Calabi-Yau threefolds ⋮ On the Atkin and Swinnerton-Dyer type congruences for some truncated hypergeometric ${}_1F_0$ series

Uses Software

• Magma
• LMFDB

Cites Work

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• \(p\)-adic cycles
• Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds
• On a supercongruence conjecture of Rodriguez-Villegas
• On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle.
• A modular supercongruence for _6F_5: An Apéry-like story

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