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Mathematics of Computation

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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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Article copyright: © Copyright 1986 American Mathematical Society

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