Effective Irrationality Measures and Approximation by Algebraic Conjugates

TL;DR

This paper develops effective irrationality measures for algebraic numbers using algebraic conjugates, generalizing Thue's Fundamental Theorem to improve approximation techniques.

Contribution

It introduces a novel approach to derive effective irrationality measures by leveraging algebraic conjugates, extending Thue's Fundamental Theorem.

Findings

Established new bounds for algebraic number approximations.

Generalized Thue's Fundamental Theorem for broader classes of algebraic numbers.

Provided a framework for constructing sequences of algebraic conjugate approximations.

Abstract

In this paper, we present a result on using algebraic conjugates to form a sequence of approximations to an algebraic number, and in this way obtain effective irrationality measures for related algebraic numbers. From this result, we are able to generalise Thue's Fundamentaltheorem.