On the Atkin and Swinnerton-Dyer type congruences for some truncated hypergeometric ${}_1F_0$ series

DOI10.4064/aa200405-8-8zbMath1478.11006arXiv1810.09370OpenAlexW3118074680MaRDI QIDQ4988873

Hao Pan, Yong Zhang

Publication date: 20 May 2021

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09370

zbMATH Keywords

binomial coefficientLucas sequencetruncated hypergeometric functionAtkin and Swinnerton-Dyer type congruence

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (2)

Proof of a Dwork-type supercongruence by induction ⋮ Supercongruences involving Lucas sequences

Cites Work

• Unnamed Item
• A \(p\)-adic supercongruence for truncated hypergeometric series \({}_7F_6\)
• Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences
• Supercongruences of Atkin and Swinnerton-Dyer type for Legendre polynomials
• New congruences for central binomial coefficients
• Some congruences for the Apéry numbers
• Hypergeometric supercongruences
• Supercongruences occurred to rigid hypergeometric type Calabi-Yau threefolds
• Supercongruences for sporadic sequences
• Atkin and Swinnerton-Dyer congruences and noncongruence modular forms
• Using the “Freshman′s Dream” to Prove Combinatorial Congruences
• A modular supercongruence for _6F_5: An Apéry-like story
• CONGRUENCES FOR TRUNCATED HYPERGEOMETRIC SERIES

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