<p>There are lots of applications to transcendence in finite characteristic.  Christol's theorem makes it possible to give proofs of theorems about transcendence of formal power series using the tools of formal language theory.  This was pioneered by Allouche, Valerie Berthe in her thesis, etc.</p>

CC BY-SA 4.0
2018-12-08T18:44:46.430Z
2018-12-08T18:44:46.430Z
Jeffrey Shallit
<p>I'm looking forward to know about applications of Christol theorem mentioned in Jefrrey Shallit's <em>Number theory and formal languages</em>. One of them is purely algebraic: if <span class="math-container">$f, g \in \mathbb{F}_q[[z]]$</span> are algberaic then their Hadamard product <span class="math-container">$f \odot g$</span> is also algebraic.</p>

<p>Can you name other applications?</p>

<co.combinatorics><automata-theory>
Applications of Christol theorem
DG_
# Applications of Christol theorem

(Asked by: username_0 on 2018-12-03)

I'm looking forward to know about applications of Christol theorem mentioned in Jefrrey Shallit's *Number theory and formal languages*. One of them is purely algebraic: if $f, g \in \mathbb{F}\_q[[z]]$ are algberaic then their Hadamard product $f \odot g$ is also algebraic.

Can you name other applications?

**Tags:** co.combinatorics, automata-theory


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## 1 answers

### Answer by username_1 on 2018-12-08. Score: 7

There are lots of applications to transcendence in finite characteristic. Christol's theorem makes it possible to give proofs of theorems about transcendence of formal power series using the tools of formal language theory. This was pioneered by Allouche, Valerie Berthe in her thesis, etc.


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