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Uniformly Diophantine numbers in a fixed real quadratic field

Published online by Cambridge University Press:  01 July 2009

Curtis T. McMullen
Curtis T. McMullen*
Affiliation:
Mathematics Department, Harvard University, 1 Oxford St, Cambridge, MA 02138-2901, USA
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Abstract

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The field contains the infinite sequence of uniformly bounded continued fractions and similar patterns can be found in 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.

Keywords

continued fractionsidealsclosed geodesicspacking constants
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 4 , July 2009 , pp. 827 - 844
Copyright
Copyright © Foundation Compositio Mathematica 2009

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