A sharper multivariate Christol's theorem with applications to diagonals and Hadamard products
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Christol's theorem
automatic sequences
algebraic power series
diagonals
Hadamard products
ANR Project
Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018
Origin
Hal imported