A generalised Kummer's Conjecture

2009/08/06 by M. J. R. MYERS, Myers, Marilyn
Mathematics · #Advanced Mathematical Identities #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.0908.0879

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.

Related

• The first factor of the class number of the p-th cyclotomic field
• Real cyclotomic fields of prime conductor and their class numbers
• Computation of the Kummer ratio of the class number for prime cyclotomic fields
• Infinite class field tower with small root discriminant
• Unit Reducible Cyclotomic Fields