We give an automata-theoretic description of the algebraic closure of the rational function field Fq(t) over a finite field Fq, generalizing a result of Christol. The description takes place within the Hahn-Mal’cev-Neumann field of “generalized power series” over Fq. Our approach includes a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a fini...

We give an automata-theoretic description of the algebraic closure of the rational function field Fq(t) over a finite field Fq, generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over Fq. In passing, we obtain a characterization of wellordered sets of rational numbers whose base p expansions are generated by a finite aut...

In this paper we give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improv...

R. Taalat [email protected] Institut d’Electronique du Sud, UMR-CNRS 5214, Université Montpellier 2, Place Eugne Bataillon, 34095 Montpellier Cedex 5, France M. Delmas [email protected] Institut d’Electronique du Sud, UMR-CNRS 5214, Université Montpellier 2, Place Eugne Bataillon, 34095 Montpellier Cedex 5, France J.-B. Rodriguez [email protected] Institu...

Benign follicular tumors comprise a large and heterogeneous group of neoplasms that share a common histogenesis and display morphological features resembling one or several portions of the normal hair follicle, or recapitulate part of its embryological development. Most cases present it as clinically nondescript single lesions and essentially of dermatological relevance. Occasionally, however, ...