Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Gauss’s ternary form reduction and the $2$-Sylow subgroup

Author: Daniel Shanks
Journal: Math. Comp. 25 (1971), 837-853
MSC: Primary 12A99
Corrigendum: Math. Comp. 32 (1978), 1328-1329.
Corrigendum: Math. Comp. 32 (1978), 1328-1329.
MathSciNet review: 0297737
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An algorithm is developed for determining the 2-Sylow subgroup of the class group of a quadratic field provided the complete factorization of the discriminant d is known. It uses Gauss’s ternary form reduction with some new improvements and is applicable even if d is so large that the class number $h(d)$ is inaccessible. Examples are given for various d that illustrate a number of special problems.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A99

Retrieve articles in all journals with MSC: 12A99

Additional Information

Keywords: Quadratic field, class group, 2-Sylow subgroup, genera, principal genus, ambiguous forms, reduction of ternary quadratic forms, cycle graph
Article copyright: © Copyright 1971 American Mathematical Society