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
Recommended Citation
Kibelbek, J., Long, L., Moss, K., Sheller, B., & Yuan, H. (2016). Supercongruences and complex multiplication. Journal of Number Theory, 164, 166-178. https://doi.org/10.1016/j.jnt.2015.12.013
