Uniformly Diophantine Numbers in a Fixed Real Quadratic Field
| 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. |
| Full Text & Related Files: |
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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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