Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Some remarks on Cohen-Lenstra heuristics

Author: Lawrence C. Washington
Journal: Math. Comp. 47 (1986), 741-747
MSC: Primary 11R11; Secondary 11Y40
MathSciNet review: 856717
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Cohen and Lenstra have given a heuristic model which predicts the fraction of imaginary quadratic fields with class number divisible by a given odd prime p and of those whose class groups have a given p-rank. We show that these numbers also arise by considering the proportion of matrices in $ {\text{GL}_n}({\mathbf{Z}}/p{\mathbf{Z}})$ with 1 as an eigenvalue and those whose 1-eigenspaces have a given dimension, then letting $ n \to \infty $. In the last section we discuss some relations with elliptic curves.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R11, 11Y40

Retrieve articles in all journals with MSC: 11R11, 11Y40

Additional Information

PII: S 0025-5718(1986)0856717-9
Article copyright: © Copyright 1986 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia