Diophantine chains
نویسندگان
چکیده
منابع مشابه
Diophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
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This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...
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R.G. Halburd∗ Department of Mathematical Sciences, Loughborough University Loughborough, Leicestershire, LE11 3TU, UK (Dated: January 21, 2005) Abstract The heights of iterates of the discrete Painlevé equations over number fields appear to grow no faster than polynomials while the heights of generic solutions of non-integrable discrete equations grow exponentially. This gives rise to a simple ...
متن کاملSome remarks on diophantine equations and diophantine approximation
We give many equivalent statements of Mahler’s generalization of the fundamental theorem of Thue. In particular, we show that the theorem of Thue–Mahler for degree 3 implies the theorem of Thue for arbitrary degree ≥ 3, and we relate it with a theorem of Siegel on the rational integral points on the projective line P(K) minus 3 points. Classification MSC 2010: 11D59; 11J87; 11D25
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A Diophantine figure, see i.e. [4, 5, 6], is a set of points on the integer grid Z where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in Z (the coordinates) and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diopha...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1983
ISSN: 0035-7596
DOI: 10.1216/rmj-1983-13-1-55