On the Mean 3-Rank of Quadratic Fields
Author: Belabas, K.
Source: Compositio Mathematica, Volume 118, Number 1, August 1999 , pp. 1-9(9)
Abstract:The Cohen–Lenstra–Martinet heuristics give precise predictions about the class groups of a `random' number field. The 3-rank of quadratic fields is one of the few instances where these have been proven. We prove that, in this case, the rate of convergence is at least sub-exponential. In addition, we show that the defect appearing in Scholz's mirror theorem is equidistributed with respect to a twisted Cohen–Lenstra density.
Document Type: Regular Paper
Affiliations: Université Paris-Sud, Département de Mathématiques (bât.42S), F-91405 Orsay, France e-mail: Karim.Belabas@math.u-psud.fr
Publication date: August 1, 1999