Algebraic Independence Measures for Values of E-functions and M-functions

TL;DR

This paper develops inequalities to measure how algebraically independent the values of E-functions and M-functions are at algebraic points, advancing understanding in transcendence theory.

Contribution

It introduces Liouville-type inequalities for Siegel E-functions and Mahler M-functions evaluated at algebraic points, extending previous transcendence results.

Findings

Liouville-type inequalities established for E-functions

Comparable inequalities derived for M-functions

Enhances tools for studying algebraic independence of special functions

Abstract

In this article, we establish a Liouville-type inequality for polynomials evaluated at the values of arbitrary Siegel E-functions at non-zero algebraic points. Additionally, we provide a comparable result within the framework of Mahler M -functions.