About Jarník’s-type relation in higher dimension

Antoine Marnat

Research output: Contribution to journalArticlepeer-review

Abstract

Using the Parametric Geometry of Numbers introduced recently by W. M. Schmidt and L. Summerer and results by D. Roy, we show that German’s transference inequalities between the two most classical exponents of uniform Diophantine approximation are optimal. Further, we establish that the n uniform exponents of Diophantine approximation in dimension are algebraically independent. Thus, no Jarník’s-type relation holds between them.
Original languageEnglish
Pages (from-to)131-150
JournalAnnales de l’Institut Fourier
Volume68
Issue number1
DOIs
Publication statusPublished - 2018

Keywords

  • Parametric geometry of numbers
  • Uniform exponents of Diophantine approximation
  • Transference inequalities

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