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

Antoine Marnat

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

Number Theory 2018-03-26 v2

Authors: Antoine Marnat

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.

Keywords

diophantine approximation classical exponents uniform exponents spectrum parametric geometry of numbers higher dimensions

Cite

@article{arxiv.1701.01584,
  title  = {Note on the spectrum of classical and uniform exponents of Diophantine approximation},
  author = {Antoine Marnat},
  journal= {arXiv preprint arXiv:1701.01584},
  year   = {2018}
}

Comments

7 pages

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