A supercongruence motivated by the Legendre family of elliptic curves

DOI10.1134/S0001434610090324zbMath1252.11017OpenAlexW2022447517MaRDI QIDQ650321

Heng Huat Chan, Wadim Zudilin, Ling Long

Publication date: 25 November 2011

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434610090324

zbMATH Keywords

finite fieldelliptic curveLegendre transformHasse invariantsupercongruenceramified double cover

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (6)

Supercongruences and complex multiplication ⋮ Factors of some truncated basic hypergeometric series ⋮ On some hypergeometric supercongruence conjectures of Long ⋮ Some \(q\)-analogues of supercongruences of Rodriguez-Villegas ⋮ Supercongruences for rigid hypergeometric Calabi-Yau threefolds ⋮ CONGRUENCES FOR TRUNCATED HYPERGEOMETRIC SERIES

Cites Work

• Unnamed Item
• A \(p\)-adic analogue of a formula of Ramanujan
• Ramanujan-type supercongruences
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Gaussian Hypergeometric series and supercongruences
• Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs
• A Gaussian hypergeometric series evaluation and Apéry number congruences

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