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

Volume 185 / 2018

Antoine Marnat Acta Arithmetica 185 (2018), 1-8 MSC: 11J13, 11K60. DOI: 10.4064/aa170106-23-3 Published online: 25 June 2018

Abstract

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.

Authors

  • Antoine MarnatDepartment of Mathematics
    University of York
    Heslington, York, YO10 5DD, United Kingdom
    e-mail

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