Uniformly Diophantine numbers in a fixed real quadratic field
نویسندگان
چکیده
منابع مشابه
Uniformly Diophantine numbers in a fixed real quadratic field
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 i...
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Let A,D, K, k ∈ N with D square free and 2 | /k, B = 1, 2 or 4 and μi ∈ {−1, 1}(i = 1, 2), and let h(−21−eD)(e = 0 or 1) denote the class number of the imaginary quadratic field Q( √−21−eD). In this paper, we give the all-positive integer solutions of the Diophantine equation Ax +μ1B = K ( (Ay +μ2B)/K )n , 2 | / n, n > 1 and we prove that if D > 1, then h(−21−eD) ≡ 0(mod n), where D, and n sati...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2009
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x09004102