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The parity of the class number
of the cyclotomic fields of prime conductor

Author: Pietro Cornacchia
Journal: Proc. Amer. Math. Soc. 125 (1997), 3163-3168
MSC (1991): Primary 11R29, 11R18; Secondary 11R27
MathSciNet review: 1401730
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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 $\chi $-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

Received by editor(s): January 18, 1996
Received by editor(s) in revised form: May 17, 1996
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society