Factors of generalized Rudin-Shapiro sequences. (Facteurs des suites de Rudin-Shapiro généralisées.)
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Finite automata and arithmetic.
Fonctions digitales le long des nombres premiers
In a recent work we gave some estimations for exponential sums of the form , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.
Formules sommatoires et systèmes de numération liés aux substitutions
Frontière du fractal de Rauzy et système de numération complexe