A generalised Kummer's Conjecture

Details A generalised Kummer's Conjecture A generalised Kummer's Conjecture

2009-08-06

arxiv.org/abs/0908.0879v1

Mathematics

Number Theory

19 pages, to appear in Glasgow Mathematical Journal

Scientific paper

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.

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