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The parity of the class number of the cyclotomic fields of prime conductor
Author(s):
Pietro
Cornacchia
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3163-3168.
MSC (1991):
Primary 11R29, 11R18;
Secondary 11R27
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Abstract:
Using a duality result for cyclotomic units proved by G.Gras, we derive a relation between the vanishing of some  -components of the ideal class groups of abelian fields of prime conductor (Theorem 1). As a consequence, we obtain a criterion for the parity of the class number of any abelian number field of prime conductor.
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Additional Information:
Pietro
Cornacchia
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
Email:
cornac@gauss.dm.unipi.it
DOI:
10.1090/S0002-9939-97-03909-9
PII:
S 0002-9939(97)03909-9
Received by editor(s):
January 18, 1996
Received by editor(s) in revised form:
May 17, 1996
Communicated by:
William W. Adams
Copyright of article:
Copyright
1997,
American Mathematical Society
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