Congruences for generalized Apéry numbers and Gaussian hypergeometric series

DOI10.1007/S40993-016-0069-ZzbMath1358.11013OpenAlexW2576524498WikidataQ114218135 ScholiaQ114218135MaRDI QIDQ515999

Gautam Kalita, Arjun Singh Chetry

Publication date: 17 March 2017

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-016-0069-z

zbMATH Keywords

Gaussian hypergeometric seriessupercongruencesApéry numbers

Mathematics Subject Classification ID

Finite fields (field-theoretic aspects) (12E20) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (4)

Beukers-like supercongruences for generalized Apéry numbers ⋮ Transformations for Appell series over finite fields and traces of Frobenius for elliptic curves ⋮ Values of Gaussian hypergeometric series and their connections to algebraic curves ⋮ Sequences, modular forms and cellular integrals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic curves and special values of Gaussian hypergeometric series
• On the Picard-Fuchs equation and the formal Brauer group of certain elliptic \(K3\)-surfaces
• Congruence properties of Apéry numbers
• Some congruences for Apery numbers
• Hypergeometric series over finite fields and Apéry numbers
• Gauss sums and the p-adic \(\Gamma\)-function
• Another congruence for the Apéry numbers
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Hyperelliptic curves and values of Gaussian hypergeometric series
• Supercongruences for sporadic sequences
• Hypergeometric functions over 𝔽_{𝕢} and traces of Frobenius for elliptic curves
• CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES
• Gaussian Hypergeometric series and supercongruences
• Super congruence for the Apéry numbers
• Hypergeometric Functions Over Finite Fields
• Values of Gaussian hypergeometric series
• Values of Gaussian hypergeometric series and their connections to algebraic curves
• A Gaussian hypergeometric series evaluation and Apéry number congruences
• CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS

This page was built for publication: Congruences for generalized Apéry numbers and Gaussian hypergeometric series