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.
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 .
Accepted:
Published online:
DOI: 10.5802/jtnb.941
Classification: 37P05, 11G20, 11B85
Keywords: Arithmetic dynamics, algebraic groups, automatic sequences, finite fields.
Author's affiliations:
@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/} }
TY - JOUR TI - The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic JO - Journal de Théorie des Nombres de Bordeaux PY - 2016 DA - 2016/// SP - 301 EP - 324 VL - 28 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.941/ UR - https://www.ams.org/mathscinet-getitem?mr=3509712 UR - https://zbmath.org/?q=an%3A1393.37109 UR - https://doi.org/10.5802/jtnb.941 DO - 10.5802/jtnb.941 LA - en ID - JTNB_2016__28_2_301_0 ER -
%0 Journal Article %T The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic %J Journal de Théorie des Nombres de Bordeaux %D 2016 %P 301-324 %V 28 %N 2 %I Société Arithmétique de Bordeaux %U https://doi.org/10.5802/jtnb.941 %R 10.5802/jtnb.941 %G en %F JTNB_2016__28_2_301_0
Andrew Bridy. The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic. Journal de Théorie des Nombres de Bordeaux, Volume 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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