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Uniformly Diophantine numbers in a fixed real quadratic field
Curtis T. McMullen
Journal:

Compositio Mathematica / Volume 145 / Issue 4 / July 2009

Published online by Cambridge University Press:

01 July 2009, pp. 827-844

Print publication:

July 2009
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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.