On a Problem of Mahler Concerning the Approximation of Exponentials and Logarithms

TL;DR

This paper explores conjectural estimates and partial results related to the Diophantine approximation of logarithms of algebraic numbers, advancing understanding in this mathematical area.

Contribution

It introduces two conjectural estimates and discusses current progress and partial results on Diophantine approximation of algebraic logarithms.

Findings

Proposed two conjectural estimates on Diophantine approximation.

Reviewed the current state of research in the field.

Presented new partial results related to the conjecture.

Abstract

We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.