<p>Recently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2497_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(1/\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mi>π</mi> </mrow> </math></EquationSource> </InlineEquation>, 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 <i>p</i>-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides <i>p</i>-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.</p>

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Supercongruences Arising from Ramanujan-Sato Series

  • Angelica Babei,
  • Manami Roy,
  • Holly Swisher,
  • Bella Tobin,
  • Fang-Ting Tu

摘要

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