On some arithmetic properties of Siegel functions

DOI10.1007/s00209-008-0456-9zbMath1228.11057OpenAlexW2799994795MaRDI QIDQ846885

Ja Kyung Koo, Dong Hwa Shin

Publication date: 15 February 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-008-0456-9

zbMATH Keywords

modular unitsclass fieldsSiegel functions

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Class field theory (11R37) Dedekind eta function, Dedekind sums (11F20) Elliptic and modular units (11G16)

Related Items (22)

Modularity of Galois traces of ray class invariants ⋮ Form class groups for extended ring class fields ⋮ On some arithmetic properties of Siegel functions (II) ⋮ Primitive and totally primitive Fricke families with applications ⋮ Singular values of principal moduli ⋮ A modularity criterion for Klein forms, with an application to modular forms of level 13 ⋮ On special values of generators of modular function fields ⋮ Normal bases of ray class fields over imaginary quadratic fields ⋮ Ray class invariants over imaginary quadratic fields ⋮ Generators of the ring of weakly holomorphic modular functions for \(\Gamma _1(N)\) ⋮ Ray class fields generated by torsion points of certain elliptic curves ⋮ Some applications of modular units ⋮ Generation of ring class fields by eta-quotients ⋮ Generators of graded rings of modular forms ⋮ Computing integral points on \(X_{\mathrm{ns}}^+(p)\) ⋮ Unnamed Item ⋮ Ramanujan's function \(k(\tau)=r(\tau)r^2(2\tau)\) and its modularity ⋮ Some applications of eta-quotients ⋮ Class invariants by Siegel resolvents and the modularity of their Galois traces ⋮ Algebraic integers as special values of modular units ⋮ Primitive generators of certain class fields ⋮ Class fields generated by coordinates of elliptic curves

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• On Ramanujan's cubic continued fraction
• Self-recursion formulas satisfied by Fourier coefficients of some modular functions

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