# Heights and totally p-adic numbers

Acta Arithmetica (2015)

- Volume: 171, Issue: 3, page 277-291
- ISSN: 0065-1036

## Access Full Article

top## Abstract

top## How to cite

topLukas Pottmeyer. "Heights and totally p-adic numbers." Acta Arithmetica 171.3 (2015): 277-291. <http://eudml.org/doc/286299>.

@article{LukasPottmeyer2015,

abstract = {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.},

author = {Lukas Pottmeyer},

journal = {Acta Arithmetica},

keywords = {height bounds; arithmetic dynamics; totally p-adic numbers},

language = {eng},

number = {3},

pages = {277-291},

title = {Heights and totally p-adic numbers},

url = {http://eudml.org/doc/286299},

volume = {171},

year = {2015},

}

TY - JOUR

AU - Lukas Pottmeyer

TI - Heights and totally p-adic numbers

JO - Acta Arithmetica

PY - 2015

VL - 171

IS - 3

SP - 277

EP - 291

AB - 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.

LA - eng

KW - height bounds; arithmetic dynamics; totally p-adic numbers

UR - http://eudml.org/doc/286299

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.