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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Gauss’s ternary form reduction and the $2$-Sylow subgroup
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by Daniel Shanks PDF
Math. Comp. 25 (1971), 837-853 Request permission

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.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 837-853
  • MSC: Primary 12A99
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0297737-4
  • MathSciNet review: 0297737