Supercongruences and complex multiplication
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
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