We prove the following analogue of Silverman's results [9] for pairs of maps.
Let be an integer, a number field, and the norm of an ideal . Let be non-constant and not of the form , . Denote , , and the ℓ-th iteration of F. There are constants , depending on d and h such that the following holds.
For almost all prime ideals , there is a finite subset , such that if at least one of the sets
(1) |
Nous prouvons l'analogue suivant des résultats de Silverman [9] pour les paires d'applications.
Soit un entier, un corps de nombres, et la norme d'un idéal . Soit un polynôme non constant qui n'est pas de la forme , . Posons , et les itérés de F. Il existe des constantes , , dépendant de d et h, possédant la propriété suivante : pour presque tout idéal premier , il y a un sous-ensemble , tel que si , au moins un des ensembles
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Mei-Chu Chang 1
@article{CRMATH_2015__353_4_283_0, author = {Mei-Chu Chang}, title = {On periods modulo \protect\emph{p} in arithmetic dynamics}, journal = {Comptes Rendus. Math\'ematique}, pages = {283--285}, publisher = {Elsevier}, volume = {353}, number = {4}, year = {2015}, doi = {10.1016/j.crma.2015.01.007}, language = {en}, }
Mei-Chu Chang. On periods modulo p in arithmetic dynamics. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 283-285. doi : 10.1016/j.crma.2015.01.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.007/
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