Ramanujan's function \(k(\tau)=r(\tau)r^2(2\tau)\) and its modularity

DOI10.1515/math-2020-0105zbMath1484.11109OpenAlexW3125961406MaRDI QIDQ2053560

Yoon Kyung Park, Yoon-Jin Lee

Publication date: 29 November 2021

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/math-2020-0105

zbMATH Keywords

congruence subgroupmodular functionclass field theoryRogers-Ramanujan continued fractionKronecker's congruenceRamanujan's function $k(\tau)$

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Class field theory (11R37) Algebraic numbers; rings of algebraic integers (11R04) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (1)

Analogue of Ramanujan’s function k(τ) for the cubic continued fraction

Cites Work

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• The level 13 analogue of the Rogers-Ramanujan continued fraction and its modularity
• On some arithmetic properties of Siegel functions
• On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\)
• Arithmetic of the Ramanujan-Göllnitz-Gordon continued fraction
• The equations for modular function fields of principal congruence subgroups of prime level
• Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction
• Some modular relations for Ramanujan's function \(k(q)=r(q)r^2(q^2)\)
• Ramanujan's Theta Functions
• Modular curves and Ramanujan's continued fraction
• CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS AND APPLICATIONS
• Traces of singular values of Hauptmoduln
• Divisibility properties of coefficients of modular functions in genus zero levels

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