Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593374 | Journal of Number Theory | 2016 | 13 Pages |
Abstract
We study congruences involving truncated hypergeometric series of the formF23(1/2,1/2,1/21,1;λ)(mps−1)/2:=∑k=0(mps−1)/2((1/2)k/k!)3λk where p is a prime and m,sm,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=1s=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=1λ=1 case and confirm some other supercongruence conjectures at special values of λ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jonas Kibelbek, Ling Long, Kevin Moss, Benjamin Sheller, Hao Yuan,