Generalized Ramanujan-Sato Series Arising from Modular Forms

TL;DR

This paper introduces a new general theorem for generating Ramanujan-Sato series for 1/π using modular forms, and constructs explicit examples related to arithmetic triangle groups, including some novel cases.

Contribution

The paper presents a new general theorem for Ramanujan-Sato series and provides explicit examples connected to non-compact arithmetic triangle groups, expanding existing knowledge.

Findings

New general theorem for Ramanujan-Sato series

Explicit examples related to arithmetic triangle groups

Some examples are novel, others reproduce known results

Abstract

Motivated by work of Chan, Chan, and Liu, we obtain a new general theorem which produces Ramanujan-Sato series for $1/\pi$. We then use it to construct explicit examples related to non-compact arithmetic triangle groups, as classified by Takeuchi. Some of our examples are new, and some reproduce existing examples.