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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The nonquadratic imaginary cyclic fields
of $2$-power degrees with class numbers
equal to their genus class numbers


Author: Stéphane Louboutin
Journal: Proc. Amer. Math. Soc. 127 (1999), 355-361
MSC (1991): Primary 11R20, 11R29; Secondary 11R42
MathSciNet review: 1468198
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Abstract: It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of $2$-power degrees with class numbers equal to their genus class numbers.


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Additional Information

Stéphane Louboutin
Affiliation: Université de Caen, UFR Sciences, Département de Mathématiques, 14032 Caen cedex, France
Email: loubouti@math.unicaen.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04548-7
PII: S 0002-9939(99)04548-7
Keywords: Genus field, relative class number, class number, cyclic number field
Received by editor(s): January 31, 1997
Received by editor(s) in revised form: May 28, 1997
Communicated by: William W. Adams
Article copyright: © Copyright 1999 American Mathematical Society