Congruences for truncated hypergeometric series ${}_2{F}_1$

Abstract

Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross-Koblitz formula. In this paper, we aim to prove four supercongruences between two truncated hypergeometric series ${}_2{F}_1$. This generalizes these four Rodriguez-Villegas supercongruences.

11 pages, to appear in Bull. Aust. Math. Soc

References in corpus (4)

• Some q-analogues of supercongruences of Rodriguez-Villegas
• Proof of Sun's conjectures on integer-valued polynomials
• Supercongruences involving dual sequences
• A supercongruence involving Delannoy numbers and Schröder numbers

Cited by in corpus (3)

• Dwork-type supercongruences through a creative $q$-microscope
• Supercongruences involving dual sequences
• Supercongruences between truncated ${}_3{F}_2$ hypergeometric series