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A GENERALISED KUMMER'S CONJECTURE

Published online by Cambridge University Press:  25 August 2010

M. J. R. MYERS
M. J. R. MYERS*
Affiliation:
Department of Mathematics and Statistics, Calvin College, Grand Rapids, MI 49546, USA e-mail: mjm49@calvin.edu
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Abstract

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Kummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott–Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.

Keywords

Primary 11R18Secondary 11M20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 453 - 472
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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