Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11R29, 11R18, 11R27

Retrieve articles in all journals with MSC (1991): 11R29, 11R18, 11R27


Additional Information

Pietro Cornacchia
Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
Email: cornac@gauss.dm.unipi.it

DOI: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society