Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups
type: Item
instance of: scholarly article
title: Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups
author: Imin Chen
author: Gleb Glebov
author: Ritesh Goenka
published in: Journal of Number Theory
publication date: 2022-08-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1909.07350
review text: This paper extends ideas from prior work to derive a complete list of Chudnovsky-Ramanujan type formulae for \(1/\pi\) associated with modular curves corresponding to non-compact arithmetic triangle groups. A number of new series expansions are derived not appearing in prior literature. The paper also provides an algorithm to rigorously compute the singular values of normalized Eisenstein series of weight 2.
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11Y60
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14K20
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 7575713
zbMATH Keywords: elliptic curves
zbMATH Keywords: elliptic functions
zbMATH Keywords: elliptic integrals
zbMATH Keywords: Dedekind eta function
zbMATH Keywords: Eisenstein series
zbMATH Keywords: hypergeometric function
zbMATH Keywords: j-invariant
zbMATH Keywords: Picard-Fuchs differential equation
MaRDI profile type: Publication
OpenAlex ID: W4297729068
Wikidata QID: Q114156553
cites work: Generalizations of Clausen's Formula and algebraic transformations of Calabi–Yau differential equations
cites work: Ramanujan-like Series for 1/π2and String Theory
cites work: Q4222737
cites work: Ramanujan's Lost Notebook
cites work: Determinant identities
cites work: Exceptional sets of hypergeometric series.
cites work: Ramanujan's Series for 1/π: A Survey
cites work: Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
cites work: Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)
cites work: Eisenstein series and approximations to \(\pi\)
cites work: Q4208562
cites work: Class number three Ramanujan type series for \(1/\pi\)
cites work: Rational analogues of Ramanujan's series for 1/π
cites work: On Chudnovsky-Ramanujan type formulae
cites work: Q3791207
cites work: Q4735239
cites work: Monstrous Moonshine
cites work: Ramanujan's Theta Functions
cites work: Congruence Subgroups of PSL(2, Z) of Genus Less than or Equal to 24
cites work: Arithmetic properties of hypergeometric mirror maps and Dwork's congruences
cites work: On Kummer's Twenty-Four Solutions of the Hypergeometric Differential Equation
cites work: History of the formulas and algorithms for pi
cites work: Proof of a rational Ramanujan-type series for 1/π. The fastest one in level 3
cites work: Proof of Chudnovskys' hypergeometric series for \(1/\pi\) using Weber modular polynomials
cites work: Modular solutions to equations of generalized Halphen type
cites work: Level 17 Ramanujan-Sato series
cites work: On Poincaré's theorem for fundamental polygons
cites work: An efficient determination of the coefficients in the Chudnovskys' series for \(1/ \pi \)
cites work: On extremal rational elliptic surfaces
cites work: Q4317891
cites work: Some new series for $1/\pi$ and related congruences
cites work: Arithmetic triangle groups
cites work: Class numbers of imaginary quadratic fields
cites work: Q4079943
cites work: Ramanujan-type identities for Shimura curves
cites work: Elliptic Modular Forms and Their Applications
cites work: A MODULAR PROOF OF TWO OF RAMANUJAN’S FORMULAE FOR
cites work: Ramanujan-type formulae for $1/\pi$: A second wind?
DOI: 10.1016/J.JNT.2022.02.013
description: scientific article; zbMATH DE number 7575713