Modular curves and Ramanujan's continued fraction

DOI10.1515/CRELLE.2006.063zbMath1147.11032OpenAlexW2026740120MaRDI QIDQ3413789

Bryden Cais, Brian Conrad

Publication date: 18 December 2006

Published in: Journal fur die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2006.063

zbMATH Keywords

modular curvescircle methodRamanujan's continued fractionsingular valuesmodular polynomialsKlein formsradical towers

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Arithmetic aspects of modular and Shimura varieties (11G18) Continued fractions (11A55)

Related Items (11)

The level 13 analogue of the Rogers-Ramanujan continued fraction and its modularity ⋮ On the coefficients of certain family of modular equations ⋮ Singular moduli of \(r\)th roots of modular functions ⋮ On Ramanujan's cubic continued fraction as a modular function ⋮ Three Ramanujan continued fractions with modularity ⋮ A continued fraction of order twelve as a modular function ⋮ Modular equations for congruence subgroups of genus zero. II ⋮ A framework of Rogers-Ramanujan identities and their arithmetic properties ⋮ Arithmetic of the Ramanujan-Göllnitz-Gordon continued fraction ⋮ Modular equations for congruence subgroups of genus zero ⋮ Ramanujan's function \(k(\tau)=r(\tau)r^2(2\tau)\) and its modularity

Cites Work

• Singular values of the Rogers-Ramanujan continued fraction
• The Rogers-Ramanujan continued fraction
• Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function
• Evaluations of the Rogers–Ramanujan continued fraction R(q) by modular equations
• On the coefficients of the transformation polynomials for the elliptic modular function
• A remark on real radical extensions
• Continued fractions and modular functions

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