Elliptic units and genus theory
type: Item
instance of: scholarly article
title: Elliptic units and genus theory
zbMATH Open document ID: 0594.12007
DOI: 10.1007/BF02941485
author: Heima Hayashi
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1985-01-01T00:00:00Z
review text: The author proves results from genus theory by using analytical class number formulas and the theory of elliptic units: if K is an imaginary quadratic field and L/K a cyclic extension of prime degree \(\ell\) with d primes of K ramified in it, then \(\ell^{d-1}\) divides the quotient of class numbers \(h_ L/h_ K\) (here up to a fudge factor involving numbers of roots of unity in L and K). The author also gives results similar to \textit{H. W. Leopoldt}'s theory of ''Auflösung'' of a character [Math. Nachr. 9, 351-362 (1953; Zbl 0053.355)].
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R37
zbMATH DE Number: 3955047
zbMATH Keywords: genus theory
zbMATH Keywords: analytical class number formulas
zbMATH Keywords: elliptic units
zbMATH Keywords: imaginary quadratic field
zbMATH Keywords: cyclic extension
zbMATH Keywords: quotient of class numbers
zbMATH Keywords: character
reviewed by: Roland Gillard
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3955047