A \(p\)-adic supercongruence for truncated hypergeometric series \({}_7F_6\)

DOI10.1007/s00025-017-0744-yzbMath1428.11010arXiv1611.10188OpenAlexW3121676993MaRDI QIDQ681260

Ji-Cai Liu

Publication date: 30 January 2018

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.10188

zbMATH Keywords

hypergeometric seriessupercongruences\(p\)-adic gamma functions

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Related Items (10)

A parametric congruence motivated by Orr's identity ⋮ An extension of a supercongruence of Long and Ramakrishna ⋮ \(q\)-supercongruences from gasper and Rahman's summation formula ⋮ Some \(q\)-supercongruences from the Gasper and Rahman quadratic summation ⋮ Some \(q\)-supercongruences from the Bailey transformation ⋮ Three families of \(q\)-supercongruences from a quadratic transformation of Rahman ⋮ On some supercongruences concerning truncated hypergeometric series ⋮ Proof of a supercongruence conjecture of He ⋮ Some numeric hypergeometric supercongruences ⋮ On the Atkin and Swinnerton-Dyer type congruences for some truncated hypergeometric ${}_1F_0$ series

Cites Work

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• Hypergeometric evaluation identities and supercongruences
• Some supercongruences occurring in truncated hypergeometric series
• A \(p\)-adic analogue of a formula of Ramanujan
• Ramanujan-type supercongruences
• An extension of the Apéry number supercongruence
• A $p$-adic supercongruence conjecture of van Hamme
• Strange Evaluations of Hypergeometric Series
• Supercongruences for truncated _{𝑛+1}𝐹_{𝑛} hypergeometric series with applications to certain weight three newforms
• A Gaussian hypergeometric series evaluation and Apéry number congruences
• Certain transformations for hypergeometric series in the p-adic setting
• Supercongruences and truncated hypergeometric series
• Number Theory

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