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Glasgow Mathematical Journal (1)

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A GENERALISED KUMMER'S CONJECTURE
M. J. R. MYERS
Journal:

Glasgow Mathematical Journal / Volume 52 / Issue 3 / September 2010

Published online by Cambridge University Press:

25 August 2010, pp. 453-472

Print publication:

September 2010
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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.