An algorithm for the principal ideal problem in indefinite quaternion algebras

Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and w...

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Bibliographic Details
Published inarXiv.org
Main Author Page, Aurel
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.05.2014
Subjects
Algorithms
Decision theory
Mathematics - Number Theory
Number theory
Quaternions
Online AccessGet full text
ISSN2331-8422
DOI10.48550/arxiv.1405.6674

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Summary:Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and we present a heuristically subexponential algorithm.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1405.6674