Heights and totally p-adic numbers

• Autorzy: Lukas Pottmeyer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11S82: Non-Archimedean dynamical systems \SeeMainly{}
• 11R04: Algebraic numbers; rings of algebraic integers
• 37P30: Height functions; Green functions; invariant measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 3
• Strony: 277-291

Daty

wydano

2015

Twórcy

autor

Lukas Pottmeyer

• Fachbereich Mathematik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland

Identyfikatory

DOI

10.4064/aa171-3-5