On inhomogeneous diophantine approximation and Hausdorff dimension
โ Scribed by M. Laurent
- Publisher
- Springer US
- Year
- 2012
- Tongue
- English
- Weight
- 144 KB
- Volume
- 180
- Category
- Article
- ISSN
- 1573-8795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
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