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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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