Splitting transference inequalities with the help of Wolfgang Schmidt's parametric geometry of numbers

TL;DR

This paper extends the analysis of Diophantine inequalities by splitting Dyson's transference inequality into a chain of inequalities for intermediate exponents, utilizing Wolfgang Schmidt's parametric geometry of numbers.

Contribution

It introduces new splitting techniques for transference inequalities involving both regular and uniform Diophantine exponents, building on previous work with intermediate exponents.

Findings

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

Connected intermediate exponents to Schmidt exponents.

Extended splitting to inequalities involving uniform exponents.

Abstract

This paper is a sequel to our previous paper arXiv:1105.1554, where we defined two types of intermediate Diophantine exponents, connected them to Schmidt exponents and split Dyson's transference inequality into a chain of inequalities for intermediate exponents. Here we present splitting of some other transference inequalities involving both regular and uniform Diophantine exponents.