Construction of ray class fields by elliptic units

DOI10.5802/jtnb.209zbMath0902.11047OpenAlexW2042333717MaRDI QIDQ1388993

Reinhard Schertz

Publication date: 21 September 1998

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1997__9_2_383_0

zbMATH Keywords

imaginary quadratic fieldray class fieldelliptic unitnormalized Klein form

Mathematics Subject Classification ID

Units and factorization (11R27) Class field theory (11R37) Elliptic and modular units (11G16)

Related Items (13)

Generation of class fields by using the Weber function ⋮ On some arithmetic properties of Siegel functions (II) ⋮ Weber's class invariants revisited ⋮ Singular moduli of \(r\)th roots of modular functions ⋮ Normal bases of ray class fields over imaginary quadratic fields ⋮ Ray class invariants over imaginary quadratic fields ⋮ An explicit factorization formula for the singular values of \(\varphi \) and the generalized principal ideal theorem ⋮ Ray class fields generated by torsion points of certain elliptic curves ⋮ Generation of ring class fields by eta-quotients ⋮ Class invariants and cyclotomic unit groups from special values of modular units ⋮ A survey of computational class field theory ⋮ Noncyclotomic Z_p-Extensions of Imaginary Quadratic Fields ⋮ Lower powers of elliptic units

Cites Work

• Zur expliziten Berechnung von Ganzheitsbasen in Strahlklassenkörpern über einem imaginär-quadratischen Zahlkörper. (On the explicit calculation of integral bases in ray class fields over an imaginary quadratic number field)
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Galoismodulstruktur und elliptische Funktionen. (Galois module structure and elliptic functions)
• Some applications of Kronecker's limit formulas
• Problèmes de construction en multiplication complexe
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