Soit un corps algébriquement clos de caractéristique positive. Nous déterminons la rationalité ou la transcendance de la fonction zêta d’Artin-Mazur d’une fonction dynamiquement affine .
We determine the rationality or the transcendence of the Artin-Mazur zeta function of a dynamically affine self-map of for an algebraically closed field of positive characteristic.
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.941
Classification : 37P05, 11G20, 11B85
Mots clés : Arithmetic dynamics, algebraic groups, automatic sequences, finite fields.
@article{JTNB_2016__28_2_301_0,
author = {Andrew Bridy},
title = {The {Artin-Mazur} {Zeta} {Function} of a {Dynamically} {Affine} {Rational} {Map} in {Positive} {Characteristic}},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {301--324},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {28},
number = {2},
year = {2016},
doi = {10.5802/jtnb.941},
mrnumber = {3509712},
zbl = {1393.37109},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.941/}
}
Andrew Bridy. The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic. Journal de Théorie des Nombres de Bordeaux, Tome 28 (2016) no. 2, pp. 301-324. doi : 10.5802/jtnb.941. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.941/
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