Uniformly Diophantine numbers in a fixed real quadratic field
نویسنده
چکیده
The field Q( √ 5) contains the infinite sequence of uniformly bounded continued fractions [1, 4, 2, 3], [1, 1, 4, 2, 1, 3], [1, 1, 1, 4, 2, 1, 1, 3] . . ., and similar patterns can be found in Q( √ 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.
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