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arxiv: 1904.08416 · v1 · pith:K7ASRLB3new · submitted 2019-04-17 · 🧮 math.NT

Hausdorff and packing dimension of Diophantine sets

classification 🧮 math.NT
keywords diophantinedimensionexponentshausdorffpackingsetsapproximationbesicovitch
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Using the variational principle in parametric geometry of numbers, we compute the Hausdorff and packing dimension of Diophantine sets related to exponents of Diophantine approximation, and their intersections. In particular, we extend a result of Jarn\'ik and Besicovitch to intermediate exponents.

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