Supercongruences Arising from Ramanujan-Sato Series

Document Type

Article

Publication Date

9-1-2025

Abstract

Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for 1/π, and used this to construct 11 explicit examples of Ramanujan-Sato series arising from modular forms for arithmetic triangle groups of non-compact type. Here, we use work of Chisholm, Deines, Long, Nebe and the third author to prove a general p-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides p-adic analogues of these Ramanujan-Sato series. We further use this theorem to construct explicit examples related to each of our explicit Ramanujan-Sato series examples.

Publication Source (Journal or Book title)

Results in Mathematics

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