An introduction to Mahler's method for transcendence and algebraic independence

TL;DR

This paper surveys Mahler's method, a technique in transcendence theory, emphasizing its applications to the arithmetic of periods of Anderson t-motives, and discusses recent developments in algebraic independence.

Contribution

It provides a comprehensive overview of Mahler's method and highlights new applications to the arithmetic of periods of Anderson t-motives.

Findings

Mahler's method effectively addresses transcendence problems.

Applications to Anderson t-motives reveal new algebraic independence results.

The survey connects classical theory with modern arithmetic applications.

Abstract

Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.