Thue's Fundamentaltheorem, I: The General Case

TL;DR

This paper analyzes Thue's Fundamentaltheorem, demonstrating its strength in providing effective irrationality measures, extending its applicability to new algebraic number families and imaginary quadratic fields.

Contribution

It shows that Thue's Fundamentaltheorem encompasses and enhances existing methods and applies to previously unconsidered algebraic numbers and imaginary quadratic fields.

Findings

Includes and strengthens hypergeometric method results

Applies to new families of algebraic numbers

Extends to imaginary quadratic number fields

Abstract

In this paper, Thue's Fundamentaltheorem is analysed. We show that it includes, and often strengthens, known effective irrationality measures obtained via the so-called hypergeometric method as well as showing that it can be applied to previously unconsidered families of algebraic numbers. Furthermore, we extend the method to also cover approximation by algebraic numbers in imaginary quadratic number fields.