Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant

Pierre Barrucand, John Harold Loxton and Hugh C. Williams

Vol. 128 (1987), No. 2, 209–222

DOI: 10.2140/pjm.1987.128.209

Abstract

Explicit upper bounds are developed for the class number and the regulator of any cubic field with a negative discriminant. Lower bounds on the class number are also developed for certain special pure cubic fields.

Mathematical Subject Classification 2000

Primary: 11R16

Secondary: 11R29

Milestones

Received: 18 May 1986

Published: 1 June 1987