More on inhomogeneous diophantine approximation
نویسندگان
چکیده
منابع مشابه
A Note on Metric Inhomogeneous Diophantine Approximation
An inhomogeneous version of a general form of the Jarn k-Besicovitch Theorem is proved. Dedicated to Professor F. Chong for his 80th birthday 1. Introduction In some respects, inhomogeneous Diophantine approximation is rather diierent from homogeneous Diophantine approximation. Results in the former, where the additional variables ooer extràdegrees of freedom', are sometimes sharper or easier t...
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In 1998, Kleinbock & Margulis [KM98] established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous Diophantine exponent w0(x) = 1/n for almost every point x on a non-degenerate submanifold M of Rn. In this paper the simultaneous inhomogeneous analogue of Sp...
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– In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the exponent of approximation to a generic point in R n by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent associate...
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Let be a strictly positive monotonically decreasing function deened on the set of positive integers. Given real numbers and , consider the solubility of the following two inequalities jq + pj < (q); (1) jq + p + j < (q) (2) for integers p and q. The rst problem is said to be homogeneous and the second inho-mogeneous (see 2]). The well known theorem of Khintchine 2, 4] asserts that for almost al...
متن کاملInhomogeneous Diophantine approximation with general error functions
Let α be an irrational and φ : N → R be a function decreasing to zero. For any α with a given Diophantine type, we show some sharp estimations for the Hausdorff dimension of the set Eφ(α) := {y ∈ R : ‖nα− y‖ < φ(n) for infinitely many n}, where ‖ · ‖ denotes the distance to the nearest integer.
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2001
ISSN: 1246-7405
DOI: 10.5802/jtnb.337