Torsion points and the Lattes family

2013/11/07 by Laura DeMarco, Xiaoguang Wang, DeMarco, Laura +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1311.1792

Theorem 1.3 now states the strongest form of the main theorem, the result of combining our methods with the conclusions of Masser-Zannier, for rational points with complex coefficients. To appear, American Journal of Math

arxiv created 2014/10/28 · arxiv updated 2014/10/29

Abstract

We give a dynamical proof of a result of Masser and Zannier [MZ2, MZ3] about torsion points on the Legendre family of elliptic curves. Our methods also treat points of small height. A key ingredient is the arithmetic equidistribution theorem on ℙ¹ of Baker-Rumely, Chambert-Loir, and Favre-Rivera-Letelier. Torsion points on the elliptic curve coincide with preperiodic points for the degree-4 Lattes family of rational functions. Our main new results concern properties of the bifurcation measures for this Lattes family associated to marked points.

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