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Mathematics of Computation

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On the $3$-Sylow subgroup of the class group of quadratic fields


Authors: Pascual Llorente and Jordi Quer
Journal: Math. Comp. 50 (1988), 321-333
MSC: Primary 11R11; Secondary 11R29
DOI: https://doi.org/10.1090/S0025-5718-1988-0917838-7
MathSciNet review: 917838
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Abstract: In this paper we give a large number of quadratic fields ${\mathbf {Q}}(\sqrt d )$ whose class group $H(d)$ has 3-Sylow subgroup ${H_3}(d)$ with rank ${r_3}(d) > 1$. They include 20 discriminants $d < 0$ with ${r_3}(d) = 5$. The associate real fields have ${r_3}(d’ ) = 4$. The distribution of the ${H_3}(d)$ is studied and its relative frequency is compared with the heuristic conjectures of Cohen and Lenstra. Some of the $H(d)$ are recorded since they are of special interest. Some related topics are also considered.


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Keywords: Quadratic fields, class group
Article copyright: © Copyright 1988 American Mathematical Society