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Mathematics of Computation

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The distribution of ideal class numbers of real quadratic fields

Author: M. D. Hendy
Journal: Math. Comp. 29 (1975), 1129-1134
MSC: Primary 12A25; Secondary 12A50
Corrigendum: Math. Comp. 30 (1976), 679.
Corrigendum: Math. Comp. 30 (1976), 679.
MathSciNet review: 0409402
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Abstract: A table of class numbers of real quadratic number fields $ Q(\surd d)$ with square-free determinant d, $ 1000 < d < 100000$ is examined and several analyses of the distribution of the class numbers, and the number of classes per genus are made. From these, two conjectures on the possible distribution of the class numbers as $ d \to \infty $ are made, which are consistent with Gauss's related conjecture.

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Keywords: Ideal classes, continued-fraction expansion, Lagrange algorithm, ideal genera, Dirichlet series, fundamental unit
Article copyright: © Copyright 1975 American Mathematical Society