Document type
ArticleVersion
Published versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193371
Continued fractions in 2-stage Euclidean quadratic fields
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
Abstract. We discuss continued fractions on real quadratic number fields of class number 1. If the field has the property of being 2-stage euclidean, a generalization of the euclidean algorithm can be used to compute these continued fractions. Although it is conjectured that all real quadratic fields of class number 1 are 2-stage euclidean, this property has been proven for only a few of them. The main result of this paper is an algorithm that, given a real quadratic field of class number 1 , verifies this conjecture, and produces as byproduct enough data to efficiently compute continued fraction expansions. If the field was not 2-stage euclidean, then the algorithm would not terminate. As an application, we enlarge the list of known 2-stage euclidean fields, by proving that all real quadratic fields of class number 1 and discriminant less than 8000 are 2-stage euclidean.
Subject (English)
Citation
Citation
GUITART MORALES, Xavier and MASDEU, Marc. Continued fractions in 2-stage Euclidean quadratic fields. Mathematics of Computation. 2013. Vol. 82, num. 282, pags. 1223-1233. ISSN 0025-5718. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/193371