Note on the spectrum of classical and uniform exponents of Diophantine approximation
Volume 185 / 2018
Acta Arithmetica 185 (2018), 1-8 MSC: 11J13, 11K60. DOI: 10.4064/aa170106-23-3 Published online: 25 June 2018
Using the parametric geometry of numbers introduced recently by W. M. Schmidt and L. Summerer (2009, 2013) and results by D. Roy (2015, 2016), we establish that the $2n$ exponents of Diophantine approximation in dimension $n\geq 3$ are algebraically independent.