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

TL;DR

This paper introduces intermediate Diophantine exponents using Schmidt and Summerer's parametric geometry of numbers, generalizing Dyson's transference inequality into a chain of inequalities.

Contribution

It develops a new framework for intermediate exponents, extending Dyson's inequality and generalizing Laurent and Bugeaud's results for Khintchine's inequalities.

Findings

Defined intermediate Diophantine exponents.

Split Dyson's transference inequality into a chain of inequalities.

Generalized Laurent and Bugeaud's results.

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.