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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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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  • FAS Scholarly Articles [7219]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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