Effective Approximation to Complex Algebraic Numbers by Algebraic Numbers of Bounded Degree

TL;DR

This paper provides the first effective improvements on the Liouville inequality, enhancing approximation bounds for complex non-real algebraic numbers using algebraic numbers of degree at most 4.

Contribution

It introduces new effective bounds for approximating complex algebraic numbers of degree at most 4, improving upon classical inequalities.

Findings

Effective bounds for approximation improved

First explicit bounds for degree 4 algebraic numbers

Enhanced understanding of algebraic number approximation

Abstract

We establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most 4.