Abstract
Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer [17, 18] and results by D. Roy [13, 14], 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 n are algebraically independent. Thus, no Jarnik's-type relation holds between them.
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