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

2025/02/14 by Faverjon, Colin, Adamczewski, Boris
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.09999

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.

Related

• Values of E-functions are not Liouville numbers
• Effective algebraic independence of values of E-functions
• Algebraic independence and normality of the values of Mahler's functions
• A Lindemann-Weierstrass theorem for E-functions
• Algebraic independence of certain Mahler numbers