Linear independence measure of logarithms over affine groups

TL;DR

This paper initiates the study of linear forms in logarithms over affine noncommutative algebraic groups, extending the theory beyond the well-understood commutative case.

Contribution

It introduces the first steps towards understanding linear independence measures of logarithms over affine noncommutative algebraic groups.

Findings

Foundation for linear forms in logarithms over affine groups established

Preliminary results suggest parallels with commutative cases

Framework opens avenues for further research in noncommutative algebraic groups

Abstract

Linear forms in logarithms over connected commutative algebraic groups over the algebraic numbers field have been studied widely. However, the theory of linear forms in logarithms over noncommutative algebraic groups have not been developed as the one of the commutative algebraic groups and in this paper we start studying linear forms in logarithms over affine groups.