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dc.contributor.author	McMullen, Curtis T.
dc.date.accessioned	2012-11-20T15:14:47Z
dc.date.issued	2009
dc.identifier.citation	McMullen, Curtis T. 2009. Uniformly Diophantine numbers in a fixed real quadratic field. Compositio Mathematica 145(4): 827-844.	en_US
dc.identifier.issn	0010-437X	en_US
dc.identifier.issn	1570-5846	en_US
dc.identifier.uri	http://nrs.harvard.edu/urn-3:HUL.InstRepos:9925390
dc.description.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.	en_US
dc.description.sponsorship	Mathematics	en_US
dc.language.iso	en_US	en_US
dc.publisher	Cambridge University Press	en_US
dc.relation.isversionof	doi:10.1112/S0010437X09004102	en_US
dc.relation.hasversion	http://www.osti.gov/eprints/topicpages/documents/record/884/2613233.html	en_US
dash.license	OAP
dc.subject	continued fractions	en_US
dc.subject	ideals	en_US
dc.subject	closed geodesics	en_US
dc.subject	packing constants	en_US
dc.title	Uniformly Diophantine Numbers in a Fixed Real Quadratic Field	en_US
dc.type	Journal Article	en_US
dc.description.version	Author's Original	en_US
dc.relation.journal	Compositio Mathematica	en_US
dash.depositing.author	McMullen, Curtis T.
dc.date.available	2012-11-20T15:14:47Z

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  Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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