{"paper":{"title":"Supercongruences and Complex Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Sheller, Hao Yuan, Jonas Kibelbek, Kevin Moss, Ling Long","submitted_at":"2012-10-16T16:57:33Z","abstract_excerpt":"We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\\lambda)_{(mp^s-1)/2} = \\sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \\lambda^k where p is a prime and m, s, r are positive integers. These truncated hypergeometric series are related to the arithmetic of a family of algebraic varieties and exhibit Atkin and Swinnerton-Dyer type congruences. In particular, when r=3, they are related to K3 surfaces. For special values of \\lambda, with s=1 and r=3, our congruences are stronger than what can be predicted by the theory of formal groups because of the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4489","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}