A finiteness property for preperiodic points of Chebyshev polynomials

2008/05/11 by Su-Ion Ih, Ih, Su-Ion, Thomas J. Tucker +1
Mathematics · #11G05 #11G35 #14G05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G05 #msc:11G35 #msc:14G05

paper · pdf · doi:10.48550/arxiv.0805.1554

12 pages

arxiv created 2008/05/11 · arxiv updated 2009/12/01

Abstract

Let K be a number field with algebraic closure K-bar, let S be a finite set of places of K containing the archimedean places, and let f be a Chebyshev polynomial. We prove that if a in K-bar is not preperiodic, then there are only finitely many preperiodic points b in K-bar which are S-integral with respect to a.

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