Note on the spectrum of classical and uniform exponents of Diophantine approximation

Antoine Marnat

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arXiv · 1701.01584

Note on the spectrum of classical and uniform exponents of Diophantine approximation

Antoine Marnat

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Abstract

Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer and results by D. Roy, we establish that the spectrum of the $2n$ exponents of Diophantine approximation in dimension $n\geq3$ is a subset of $\mathbb{R}^{2n}$ with non empty interior.

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Antoine Marnat. 2017-01-06. Note on the spectrum of classical and uniform exponents of Diophantine approximation. https://arxiv.org/abs/1701.01584

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