AbstractWe study generalized zeta functions of formal languages and series. We give necessary conditions for the rationality of the generalized zeta function. We show that it is decidable whether or not the (generalized) zeta function of a Q-algebraic series is a rational function. The same question is shown to be undecidable for context-free languages
AbstractWe give algebraic proofs of transcendence over Q(X) of formal power series with rational coe...
AbstractTwo properties of languages which are supports of rational power series are proved: (i) if t...
AbstractMotivated by arithmetic applications, we introduce the notion of a partial zeta function whi...
AbstractWe study generalized zeta functions of formal languages and series. We give necessary condit...
AbstractWe show that if the zeta function of a regular language L is rational, then there exist cycl...
AbstractWe study algebraic generalized zeta functions of formal power series. We show that the gener...
AbstractWe show that if the zeta function of a regular language L is rational, then there exist cycl...
Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix ...
AbstractWe prove that the partial zeta function introduced in [9] is a rational function, generalizi...
International audienceWe prove that cyclic languages are the boolean closure of languages called str...
We study the connections between rational series with coefficients in a semiring and their languages...
AbstractIt is proved that the generating function defined by the numbers of isomorphism classes of a...
AbstractWe study the connections between rational series with coefficients in a semiring and their l...
AbstractWe prove the rationality of various noncommutative formal power series, whose coefficients a...
International audienceWe prove that cyclic languages are the boolean closure of languages called str...
AbstractWe give algebraic proofs of transcendence over Q(X) of formal power series with rational coe...
AbstractTwo properties of languages which are supports of rational power series are proved: (i) if t...
AbstractMotivated by arithmetic applications, we introduce the notion of a partial zeta function whi...
AbstractWe study generalized zeta functions of formal languages and series. We give necessary condit...
AbstractWe show that if the zeta function of a regular language L is rational, then there exist cycl...
AbstractWe study algebraic generalized zeta functions of formal power series. We show that the gener...
AbstractWe show that if the zeta function of a regular language L is rational, then there exist cycl...
Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix ...
AbstractWe prove that the partial zeta function introduced in [9] is a rational function, generalizi...
International audienceWe prove that cyclic languages are the boolean closure of languages called str...
We study the connections between rational series with coefficients in a semiring and their languages...
AbstractIt is proved that the generating function defined by the numbers of isomorphism classes of a...
AbstractWe study the connections between rational series with coefficients in a semiring and their l...
AbstractWe prove the rationality of various noncommutative formal power series, whose coefficients a...
International audienceWe prove that cyclic languages are the boolean closure of languages called str...
AbstractWe give algebraic proofs of transcendence over Q(X) of formal power series with rational coe...
AbstractTwo properties of languages which are supports of rational power series are proved: (i) if t...
AbstractMotivated by arithmetic applications, we introduce the notion of a partial zeta function whi...
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