Hausdorff and packing dimension of Diophantine sets

Antoine Marnat

Hausdorff and packing dimension of Diophantine sets

Antoine Marnat

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article

Abstract

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.

Original language	Undefined/Unknown
Journal	arXiv.org e-Print archive
Publication status	Published - 17 Apr 2019

Keywords

math.NT

Cite this

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title = "Hausdorff and packing dimension of Diophantine sets",

abstract = "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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AU - Marnat, Antoine

PY - 2019/4/17

Y1 - 2019/4/17

N2 - 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.

AB - 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.