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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Quadratic fields with $3$-rank equal to $4$

Authors: F. Diaz y Diaz, Daniel Shanks and H. C. Williams
Journal: Math. Comp. 33 (1979), 836-840
MSC: Primary 12A25; Secondary 12A50
MathSciNet review: 521299
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Abstract: In [2] there is reference to 119 known imaginary quadratic fields that have 3-rank $r \geqslant 4$. We examine these fields and determine the exact values of r. Their associated real fields and the distribution of their 3-Sylow subgroups are also studied. Some of the class groups are recorded since they are of special interest. These include examples having an infinite class field tower and only one ramified prime, and others having an infinite tower because of two different components of their class groups.

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Article copyright: © Copyright 1979 American Mathematical Society