Ramanujan's modular equations and Atkin-Lehner involutions

DOI10.1007/BF02762264zbMath0922.11040OpenAlexW2066124438MaRDI QIDQ1279623

Heng Huat Chan, Mong-Lung Lang

Publication date: 17 June 1999

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02762264

zbMATH Keywords

congruence subgroupmodular functionAtkin-Lehner involutionRamanujan modular equations

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Dedekind eta function, Dedekind sums (11F20)

Related Items (13)

Rational analogues of Ramanujan's series for 1/π ⋮ Renormalization, isogenies, and rational symmetries of differential equations ⋮ Schwarzian conditions for linear differential operators with selected differential Galois groups ⋮ New analogues of Clausen's identities arising from the theory of modular forms ⋮ On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\) ⋮ New analogues of Ramanujan's partition identities ⋮ Mahler measures of a family of non-tempered polynomials and Boyd's conjectures ⋮ Wronskians of theta functions and series for \(1/\pi\) ⋮ Further explorations of Boyd's conjectures and a conductor 21 elliptic curve ⋮ Level 14 and 15 analogues of Ramanujan’s elliptic functions to alternative bases ⋮ Unnamed Item ⋮ Modular proofs of Gosper's identities ⋮ Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

Cites Work

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• The automorphism group of Leech lattice and elliptic modular functions
• Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations
• Some Values for the Rogers-Ramanujan Continued Fraction
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• Construction and Application of a Class of Modular Functions (II)†

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