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On inhomogeneous diophantine approximation and Hausdorff dimension

โœ Scribed by M. Laurent


Publisher
Springer US
Year
2012
Tongue
English
Weight
144 KB
Volume
180
Category
Article
ISSN
1573-8795

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A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and SwinnertonDyer. As an application, a new proof of a theorem of Davenport, which

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Let m, n be positive integers and let : Z n ร„ R be a non-negative function. Let W(m, n; ) be the set { X # R mn : " : n j=1 x ij q j " < (q), 1 i m, for infinitely many q # Z n = . The Hausdorff dimension of W(m, n; ) is obtained for arbitrary non-negative functions , with no monotonicity assumpti