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We give a dynamical construction of an infinite sequence of distinct totally $p$-adic algebraic numbers whose Weil heights tend to the limit $\frac{\log p}{p-1}$, thus giving a new proof of… Click to show full abstract
We give a dynamical construction of an infinite sequence of distinct totally $p$-adic algebraic numbers whose Weil heights tend to the limit $\frac{\log p}{p-1}$, 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 $\sigma(x)=x^2$ and $\phi_p(x)=\frac{1}{p}(x^p-x)$.
Keywords:
totally adic;
construction small;
dynamical construction;
algebraic numbers;
adic algebraic
Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Number Theory
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!