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) = x 2 and φ p (x) = 1 p (x p − x).

The height of an algebraic number α is a measure of how arithmetically complicated α is. We say α is totally p-adic if the minimal polynomial of α splits completely over the field ‫ޑ‬ p of p-adic numbers.We investigate what can be said about the smallest nonzero height of a degree 3 totally p-adic number.

No abstract

No abstract

No abstract