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.
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