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arXiv · 2408.08844

Supercongruences arising from Ramanujan-Sato Series

Angelica Babei·Manami Roy·Holly Swisher·Bella Tobin·Fang-Ting Tu
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Abstract

Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for $1/\pi$, 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.

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Angelica Babei, Manami Roy, Holly Swisher, Bella Tobin, Fang-Ting Tu. 2024-08-16. Supercongruences arising from Ramanujan-Sato Series. https://arxiv.org/abs/2408.08844

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