On linear forms and Diophantine approximation
نویسندگان
چکیده
منابع مشابه
Diophantine Approximation of Ternary Linear Forms . II
Let 6 denote the positive root of the equation xs + x2 — 2x — 1 = 0; that is, 8 = 2 cos(27r/7). The main result of the paper is the evaluation of the constant lim supm-co min M2\x + By + 02z|, where the min is taken over all integers x, y, z satisfying 1 g max (\y\, |z|) g M. Its value is (29 + 3),/7 = .78485. The same method can be applied to other constants of the same type.
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چکیده ندارد.
15 صفحه اولDiophantine 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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.90.475