ADAMCZEWSKI, Boris; BOSTAN, Alin; CARUSO, Xavier

Métadonnées

Licence d’utilisation du document

ADAMCZEWSKI, Boris
Université Claude Bernard Lyon 1 [UCBL]

BOSTAN, Alin
Calcul formel, mathématiques expérimentales et interactions [MATHEXP]

CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

Langue

Document de travail - Pré-publication

Résumé en anglais

We provide a new proof of the multivariate version of Christol's theorem about algebraic power series with coefficients in finite fields, as well as of its extension to perfect ground fields of positive characteristic obtained independently by Denef and Lipshitz, Sharif and Woodcok, and Harase. Our proof is elementary, effective, and allows for much sharper estimates. We discuss various applications of such estimates, in particular to a problem raised by Deligne concerning the algebraicity degree of reductions modulo p of diagonals of multivariate algebraic power series with integer coefficients.< Réduire

Mots clés en anglais

Christol's theorem

automatic sequences

algebraic power series

diagonals

Hadamard products

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190531

Project ANR

Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251