English

A generalised Kummer's Conjecture

Number Theory 2009-08-07 v1

Abstract

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

Cite

@article{arxiv.0908.0879,
  title  = {A generalised Kummer's Conjecture},
  author = {Marilyn Myers},
  journal= {arXiv preprint arXiv:0908.0879},
  year   = {2009}
}

Comments

19 pages, to appear in Glasgow Mathematical Journal

R2 v1 2026-06-21T13:33:07.482Z