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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
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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.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0856717-9
PII: S 0025-5718(1986)0856717-9
Article copyright: © Copyright 1986 American Mathematical Society