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On the Mean 3-Rank of Quadratic Fields

Published online by Cambridge University Press:  04 December 2007

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

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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.

Keywords

class groupsheuristics3-rankquadratic fields.
Type
Research Article
Information
Compositio Mathematica , Volume 118 , Issue 1 , August 1999 , pp. 1 - 9
Copyright
© 1999 Kluwer Academic Publishers