The conjugate property for Diophantine approximation of continued fractions
نویسندگان
چکیده
منابع مشابه
Exponents of Diophantine Approximation and Sturmian Continued Fractions
– Let ξ be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w n (ξ) and w * n (ξ) defined by Mahler and Koksma. We calculate their six values when n = 2 and ξ is a real number whose continued fraction expansion coincides with some Sturmian sequence of positive integers, up to the initial terms. In particular, we...
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We study a problem of approximate computation of color transforms (with real and possibly irrational factors) using integer arithmetics. We show that precision of such computations can be significantly improved if we allow input or output variables to be scaled by some constant. The problem of finding such a constant turns out to be related to the classic Diophantine approximation problem. We u...
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Building on the work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel’fond’s transcendence criterion which provides a sufficient condition for a complex or p-adic number ξ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at ξ together with most of their derivatives. The second one, which follows from this crit...
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In 1969, Davenport and Schmidt provided upper bounds for the approximation of a real number by algebraic integers. Their novel approach was based on the geometry of numbers and involved the duality for convex bodies. In the present thesis we study the approximation of a real number by conjugate algebraic numbers. We find inspiration in Davenport and Schmidt’s method, but ultimately our approxim...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0937852-8