A kit for linear forms in three logarithms

TL;DR

This paper introduces a new technique for deriving explicit bounds in problems involving linear forms in three complex logarithms of algebraic numbers, offering improvements over existing methods.

Contribution

The paper presents a novel technique that yields significantly better explicit bounds for linear forms in three logarithms, with demonstrated examples and publicly available code.

Findings

Improved explicit bounds for linear forms in three logarithms.

Worked examples illustrating the technique's effectiveness.

Availability of shared code for practical use.

Abstract

We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear forms in logarithms. We give worked examples to demonstrate both the use of our technique and the improvements it provides. Publicly shared code is also available.