Level 16 analogue of Ramanujan's theories of elliptic functions to alternative bases

DOI10.1016/J.JNT.2015.12.017zbMath1416.11060OpenAlexW2258378883MaRDI QIDQ266604

Dongxi Ye

Publication date: 13 April 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.12.017

zbMATH Keywords

Eisenstein seriestheta functionsDedekind's eta functionmodular equationRamanujan's theories of elliptic functions to alternative bases

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20)

Related Items (5)

A level 16 analogue of Ramanujan series for \(1/\pi\) ⋮ Ramanujan–Sato series for $1/\pi $ ⋮ ON A NEW PARAMETER INVOLVING RAMANUJAN'S THETA-FUNCTIONS ⋮ Series for \(1/\pi\) of level 20 ⋮ Elliptic integrals and Ramanujan-type series for \(1/\pi\) associated with \({\Gamma}_{0}(N)\), where \(N\) is a product of two small primes

Cites Work

• Hypergeometric transformation formulas of degrees 3, 7, 11 and 23
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• The Rogers-Ramanujan continued fraction and its level 13 analogue
• Factorizations of certain \(q\)-series identities of Ramanujan and others
• Ramanujan's Series for 1/π: A Survey
• Rational analogues of Ramanujan's series for 1/π
• THE LEVEL 12 ANALOGUE OF RAMANUJAN’S FUNCTION
• Inversion formulas for elliptic functions
• A Simple Proof of Jacobi's Four-Square Theorem
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• The computation of classical constants
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
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