How to split Dyson's transference inequality with the help of Wolfgang Schmidt's parametric geometry of numbers

2011/05/08 by German, Oleg N.
#11J13 #11J82 (Primary) 11H06 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1105.1554

Abstract

In this paper we develop some of the ideas belonging to W.Schmidt and L.Summerer to define intermediate Diophantine exponents and split Dyson's transference inequality into a chain of inequalities for intermediate exponents. This splitting generalizes the analogous result of M.Laurent and Y.Bugeaud for Khintchine's transference inequalities.

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