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On inhomogeneous diophantine approximation and Hausdorff dimension

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Abstract

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.

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  1. Institut de Mathématiques de Luminy, C.N.R.S.—U.M.R. 6206 — case 907, 163, avenue de Luminy, 13288, Marseille cedex 9, France

    M. Laurent

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  1. M. Laurent
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Correspondence to M. Laurent.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 5, pp. 93–101, 2010.

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Laurent, M. On inhomogeneous diophantine approximation and Hausdorff dimension. J Math Sci 180, 592–598 (2012). https://doi.org/10.1007/s10958-012-0658-x

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  • DOI: https://doi.org/10.1007/s10958-012-0658-x

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