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arxiv: 0805.1554 · v1 · submitted 2008-05-11 · 🧮 math.NT

A finiteness property for preperiodic points of Chebyshev polynomials

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keywords k-barpreperiodicchebyshevplacespointsalgebraicarchimedeanclosure
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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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