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

## TL;DR

This paper explores the range of classical and uniform exponents in Diophantine approximation for dimensions three and higher, showing that their spectrum has a rich structure with non-empty interior.

## Contribution

It establishes that the spectrum of 2n exponents in dimension n≥3 is a subset of R^{2n} with non-empty interior, using Parametric Geometry of Numbers and recent results.

## Key findings

- Spectrum of 2n exponents has non-empty interior for n≥3
- Utilizes Parametric Geometry of Numbers and recent theoretical results
- Extends understanding of Diophantine approximation exponents in higher dimensions

## 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.