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Heights and totally p-adic numbers

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Pottmeyer L.

Acta Arithmetica

2015

tom 171

nr 3

277-291

We study the behavior of canonical height functions $ĥ_{f}$, associated to rational maps f, on totally p-adic fields. In particular, we prove that there is a gap between zero and the next smallest value of $ĥ_{f}$ on the maximal totally p-adic field if the map f has at least one periodic point not contained in this field. As an application we prove that there is no infinite subset X in the compositum of all number fields of degree at most d such that f(X) = X for some non-linear polynomial f. This answers a question of W. Narkiewicz from 1963.

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1 Acta Arithmetica

1 Pottmeyer L.

1 2015

Wyniki wyszukiwania

Heights and totally p-adic numbers