Journal of Mathematical Sciences

, Volume 180, Issue 5, pp 592–598 | Cite as

On inhomogeneous diophantine approximation and Hausdorff dimension



Let Γ = Z A + Z n  ⊂ R n be a dense subgroup of rank n + 1 and let \( \hat{w} \)(A) denote the exponent of uniform simultaneous rational approximation to the generating point A. For any real number v ≥\( \hat{w} \)(A), the Hausdorff dimension of the set B v of points in R n that are v-approximable with respect to Γ is shown to be equal to 1/v.


Positive Real Number Hausdorff Dimension Integer Point Diophantine Approximation Dense Subgroup 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Institut de Mathématiques de LuminyC.N.R.S.—U.M.R. 6206 — case 907Marseille cedex 9France

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