Zero order estimates for Mahler functions

TL;DR

This paper provides an upper bound on the zero order of the difference between Mahler functions and algebraic functions, advancing understanding of their approximation properties.

Contribution

It introduces a new upper bound for the zero order of Mahler functions relative to algebraic functions, complementing prior polynomial evaluation estimates.

Findings

Established an upper bound for the zero order of Mahler functions.

Extended previous work by Nesterenko, Nishioka, and T"opfer.

Enhances the theoretical framework for Mahler function approximation.

Abstract

We give an upper bound for the zero order of the difference between a Mahler function and an algebraic function. This complements estimates of Nesterenko, Nishioka, and T\"opfer, among others, who considered polynomials evaluated at Mahler functions.