A dynamical construction of small totally p-adic algebraic numbers

2019/01/23 by Petsche, Clayton, Stacy, Emerald
#11G50 #37P05 #37P30 #37P50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.07661

Abstract

We give a dynamical construction of an infinite sequence of distinct totally p-adic algebraic numbers whose Weil heights tend to the limit (log p)/(p-1), thus giving a new proof of a result of Bombieri-Zannier. The proof is essentially equivalent to the explicit calculation of the Arakelov-Zhang pairing of the maps σ(x)=x² and ϕ_p(x)=(1)/(p)(x^p-x).

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