Title

Supercongruences and complex multiplication

Document Type

Article

Publication Date

7-1-2016

Abstract

We study congruences involving truncated hypergeometric series of the form. where p is a prime and m, s are positive integers. These truncated hypergeometric series are related to the arithmetic of a family of K3 surfaces. For special values of λ, with s= 1, our congruences are stronger than those predicted by the theory of formal groups, because of the presence of elliptic curves with complex multiplications. They generalize a conjecture made by Stienstra and Beukers for the λ = 1 case and confirm some other supercongruence conjectures at special values of λ.

Publication Source (Journal or Book title)

Journal of Number Theory

First Page

166

Last Page

178

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