Uniformly Diophantine Numbers in a Fixed Real Quadratic Field

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Uniformly Diophantine Numbers in a Fixed Real Quadratic Field

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Title: Uniformly Diophantine Numbers in a Fixed Real Quadratic Field
Author: McMullen, Curtis T.
Citation: McMullen, Curtis T. 2009. Uniformly Diophantine numbers in a fixed real quadratic field. Compositio Mathematica 145(4): 827-844.
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Abstract: The field \(\mathbb{Q}(\sqrt5)\) contains the infinite sequence of uniformly bounded continued fractions \([\overline{1, 4, 2, 3}], [\overline{1, 1, 4, 2, 1, 3}], [\overline{1, 1, 1, 4, 2, 1, 1, 3}]\), ..., and similar patterns can be found in \(\mathbb{Q}(\sqrt d)\) for any \(d>0\). This paper studies the broader structure underlying these patterns, and develops related results and conjectures for closed geodesics on arithmetic manifolds, packing constants of ideals, class numbers and heights.
Published Version: doi:10.1112/S0010437X09004102
Other Sources: http://www.osti.gov/eprints/topicpages/documents/record/884/2613233.html
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9925390

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  • FAS Scholarly Articles [7470]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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