Compositio Mathematica



On the Mean 3-Rank of Quadratic Fields


KARIM BELABAS a1
a1 Université Paris-Sud, Département de Mathématiques (bât.42S), F-91405 Orsay, France e-mail: Karim.Belabas@math.u-psud.fr

Article author query
belabas k   [Google Scholar] 
 

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.


Key Words: class groups; heuristics; 3-rank; quadratic fields..