Construction of normal bases by special values of Hilbert modular functions

DOI10.3792/pjaa.73.42zbMath0877.11058OpenAlexW2001553102MaRDI QIDQ1364455

Keiichi Komatsu

Publication date: 20 November 1997

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.73.42

zbMATH Keywords

normal basesHilbert modular formsHecke L-series

Mathematics Subject Classification ID

Galois representations (11F80) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Cites Work

• Unnamed Item
• Relative Galois module structure of rings of integers and elliptic functions. II
• Galoismodulstruktur und elliptische Funktionen. (Galois module structure and elliptic functions)
• On some arithmetic properties of modular forms of one and several variables
• Cyclic Galois extensions of commutative rings
• Normal bases and \(\mathbb{Z}_ p\)-extensions
• Normal basis and Greenberg's conjecture
• Modular construction of normal basis
• Construction of class fields and zeta functions of algebraic curves
• Models of certain automorphic function fields
• Relative Galois Module Structure of Rings of Integers and Elliptic Functions III
• Normal Bases of Class Fields over Gauss' Number Field
• L-functions of elliptic curves with complex multiplication, II

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