Christian Mauduit: Infinite automata and number theory

We present the notion of sequence of integers generated by an infinite automaton. The study of the combinatorial, arithmetical and statistical properties of this kind of sequences seems to be a new and difficult question. We will describe some first results in this direction obtained recently in collaboration with András Sárközy, Étienne Fouvry, Joël Rivat and Michael Drmota and we will mention several open problems.

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