The parity of the class number of the cyclotomic fields of prime conductor
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- by Pietro Cornacchia PDF
- Proc. Amer. Math. Soc. 125 (1997), 3163-3168 Request permission
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.References
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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
- Received by editor(s): January 18, 1996
- Received by editor(s) in revised form: May 17, 1996
- Communicated by: William W. Adams
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3163-3168
- MSC (1991): Primary 11R29, 11R18; Secondary 11R27
- DOI: https://doi.org/10.1090/S0002-9939-97-03909-9
- MathSciNet review: 1401730