Supercongruences for Apéry-like numbers

DOI10.1016/j.aam.2011.03.002zbMath1244.11006arXiv0906.3413OpenAlexW2949578162MaRDI QIDQ719342

Brundaban Sahu, Robert Osburn

Publication date: 10 October 2011

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3413

zbMATH Keywords

supercongruencesApéry-like numbers

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Congruences; primitive roots; residue systems (11A07)

Related Items

Divisibility properties of sporadic Apéry-like numbers ⋮ New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences ⋮ Congruences Involving Hecke-Rogers Type Series and Modular Forms ⋮ Gessel-Lucas congruences for sporadic sequences ⋮ A supercongruence for generalized Domb numbers ⋮ Modular forms, hypergeometric functions and congruences ⋮ Supercongruences for sporadic sequences ⋮ Sequences, modular forms and cellular integrals ⋮ Apéry-like numbers and families of newforms with complex multiplication ⋮ Some supercongruences on truncated hypergeometric series ⋮ CONGRUENCES AMONG POWER SERIES COEFFICIENTS OF MODULAR FORMS ⋮ Proof of two conjectures of Sun on congruences for Franel numbers ⋮ On two supercongruences involving Almkvist-Zudilin sequences

Uses Software

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Cites Work

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• On differential equations satisfied by modular forms
• On Dwork's accessory parameter problem
• CONGRUENCES RELATED TO MODULAR FORMS
• Elliptic integral evaluations of Bessel moments and applications
• Series and iterations for 1/π
• CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS