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http://hdl.handle.net/2445/193371
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DC Field | Value | Language |
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dc.contributor.author | Guitart Morales, Xavier | - |
dc.contributor.author | Masdeu, Marc | - |
dc.date.accessioned | 2023-02-09T18:49:17Z | - |
dc.date.available | 2023-02-09T18:49:17Z | - |
dc.date.issued | 2013-04 | - |
dc.identifier.issn | 0025-5718 | - |
dc.identifier.uri | http://hdl.handle.net/2445/193371 | - |
dc.description.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. | - |
dc.format.extent | 11 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Mathematical Society (AMS) | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1090/S0025-5718-2012-02620-2 | - |
dc.relation.ispartof | Mathematics of Computation, 2013, vol. 82, num. 282, p. 1223-1233 | - |
dc.relation.uri | https://doi.org/10.1090/S0025-5718-2012-02620-2 | - |
dc.rights | (c) American Mathematical Society (AMS), 2013 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria de nombres | - |
dc.subject.classification | Fraccions contínues | - |
dc.subject.classification | Àlgebra commutativa | - |
dc.subject.classification | Anells (Àlgebra) | - |
dc.subject.other | Number theory | - |
dc.subject.other | Continued fractions | - |
dc.subject.other | Commutative algebra | - |
dc.subject.other | Rings (Algebra) | - |
dc.title | Continued fractions in 2-stage Euclidean quadratic fields | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 650044 | - |
dc.date.updated | 2023-02-09T18:49:17Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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650044.pdf | 227.16 kB | Adobe PDF | View/Open |
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