# An introduction to Mahler’s method for transcendence and algebraic independence

@article{Pellarin2020AnIT, title={An introduction to Mahler’s method for transcendence and algebraic independence}, author={Federico Pellarin}, journal={\$t\$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects}, year={2020} }

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.

## 20 Citations

### A Density Theorem for the Difference Galois Groups of Regular Singular Mahler Equations

- MathematicsInternational Mathematics Research Notices
- 2021

The difference Galois theory of Mahler equations is an active research area. The present paper aims at developing the analytic aspects of this theory. We first attach a pair of connection matrices…

### INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

- MathematicsBulletin of the Australian Mathematical Society
- 2015

We study analytic properties of certain infinite products of cyclotomic polynomials that generalise some products introduced by Mahler. We characterise those that have the unit circle as a natural…

### Drinfeld A-quasi-modular forms.

- Mathematics
- 2010

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of…

### A PROBLEM ABOUT MAHLER FUNCTIONS

- Mathematics
- 2013

— Let K be a field of characteristic zero and k and l be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and van der Poorten during…

### The Many Faces of the Kempner Number

- Mathematics
- 2013

In this survey, we present five di! erent proofs for the transcendence of Kempner’s number, defined by the infinite series ! !=0 1 22n .W e take the opportunity to mention some interesting ideas and…

### On the algebraic relations between Mahler functions

- Mathematics
- 2017

In the last years, a number of authors have studied the algebraic relations between the generating series of automatic sequences. It turns out that these series are solutions of Mahler type…

### Values of certain L-series in positive characteristic

- Mathematics
- 2012

We introduce a class of deformations of the values of the Goss zeta function. We prove, with the use of the theory of deformations of vectorial modular forms as well as with other techniques, a…

### Algebraic independence and normality of the values of Mahler's functions

- Mathematics
- 2013

The main purpose of this article is to provide new results on algebraic independence of values of Mahler functions and their generalizations. Simultaneously, we establish new measures of algebraic…

### A problem around Mahler functions

- Mathematics
- 2013

Let $K$ be a field of characteristic zero and $k$ and $l$ be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and van der Poorten…

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