Heights and totally p-adic numbers

Lukas 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 -