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On preperiodic points for rational functions defined over mathbbFp(t)

Canci, Jung Kyu and Paladino, Laura. (2016) On preperiodic points for rational functions defined over mathbbFp(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 Pinmathbb(P)1(mathbbQ) be a periodic point for a monic polynomial with coefficients in mathbbZ. 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 mathbbQ with good reduction everywhere (i.e. at any finite place of mathbbQ). The set of monic polynomials with coefficients in mathbbZ can be characterized, up to conjugation by elements in PGL2(mathbbZ),asthesetofallrationalfunctionsdefinedovermathbb{Q}withatotallyramifiedfixedpointinmathbb{Q}andwithgoodreductioneverywhere.Letpbeaprimenumberandletmathbb{F}_pbethefieldwithpelements.Inthepresentpaperweconsiderrationalfunctionsdefinedovertherationalglobalfunctionfieldmathbb{F}_p(t)withgoodreductionateveryfiniteplace.Weprovesomeboundsforthecardinalityoforbitsinmathbb{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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