2024/08/16 by Babei, Angelica, Roy, Manami, Swisher, Holly +2 · 1 citation
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2408.08844
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.