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On preperiodic points for rational functions defined over $mathbb{F}_p(t)$

Canci, Jung Kyu and Paladino, Laura. (2016) On preperiodic points for rational functions defined over $mathbb{F}_p(t)$. Rivista di Matematica della Università di Parma, 7 (1). p. 12.

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Official URL: http://edoc.unibas.ch/53282/

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Abstract

Let $Pin mathbb(P)_1(mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $mathbb{Z}$. With elementary techniques one sees that the minimal periodicity of $P$ is at most 2. Recently we proved a generalization of this fact to the set of all rational functions defined over $mathbb{Q}$ with good reduction everywhere (i.e. at any finite place of $mathbb{Q}$). The set of monic polynomials with coefficients in $mathbb{Z}$ can be characterized, up to conjugation by elements in PGL$_2(mathbb{Z}), as the set of all rational functions defined over $mathbb{Q}$ with a totally ramified fixed point in $mathbb{Q}$ and with good reduction everywhere. Let $p$ be a prime number and let $mathbb{F}_p$ be the field with $p$ elements. In the present paper we consider rational functions defined over the rational global function field $mathbb{F}_p(t)$ with good reduction at every finite place. We prove some bounds for the cardinality of orbits in $mathbb{F}_pcup{infty}$ for periodic and preperiodic points.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Canci, Jung Kyu
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Università di Parma
ISSN:0035-6298
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:31 Oct 2017 10:25
Deposited On:31 Oct 2017 10:25

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