Supercongruences for sporadic sequences

Abstract

We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.

16 pages, to appear in Proceedings of the Edinburgh Mathematical Society

References in corpus (2)

• Multivariate Apéry numbers and supercongruences of rational functions
• Supercongruences and Complex Multiplication

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• Crouching AGM, Hidden Modularity
• Distribution of values of Gaussian hypergeometric functions
• Supercongruences for truncated hypergeometric series and p-adic gamma function
• Supercongruences for central trinomial coefficients
• Three supercongruences for Apery numbers or Franel numbers
• $p$-adic supercongruences conjectured by Sun
• On sporadic sequences
• Divisibility properties of sporadic Apéry-like numbers
• On the Atkin and Swinnerton-Dyer type congruences for some truncated hypergeometric ${}_1{F}_0$ series