Equidistribution and the heights of totally real and totally p-adic numbers

Paul Fili; Zachary Miner

Acta Arithmetica (2015)

  • Volume: 170, Issue: 1, page 15-25
  • ISSN: 0065-1036

Abstract

top
C. J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of the height of all totally real integers, and determining isolated values of the height. Later, Bombieri and Zannier established similar results for totally p-adic numbers and, inspired by work of Ullmo and Zhang, termed this the Bogomolov property. In this paper, we use results on equidistribution of points of low height to generalize both Bogomolov-type results to a wide variety of heights arising in arithmetic dynamics.

How to cite

top

Paul Fili, and Zachary Miner. "Equidistribution and the heights of totally real and totally p-adic numbers." Acta Arithmetica 170.1 (2015): 15-25. <http://eudml.org/doc/279353>.

@article{PaulFili2015,
abstract = {C. J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of the height of all totally real integers, and determining isolated values of the height. Later, Bombieri and Zannier established similar results for totally p-adic numbers and, inspired by work of Ullmo and Zhang, termed this the Bogomolov property. In this paper, we use results on equidistribution of points of low height to generalize both Bogomolov-type results to a wide variety of heights arising in arithmetic dynamics.},
author = {Paul Fili, Zachary Miner},
journal = {Acta Arithmetica},
keywords = {Weil height; equidistribution; totally real; totally p-adic; Fekete-Szegő theorem},
language = {eng},
number = {1},
pages = {15-25},
title = {Equidistribution and the heights of totally real and totally p-adic numbers},
url = {http://eudml.org/doc/279353},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Paul Fili
AU - Zachary Miner
TI - Equidistribution and the heights of totally real and totally p-adic numbers
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 1
SP - 15
EP - 25
AB - C. J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of the height of all totally real integers, and determining isolated values of the height. Later, Bombieri and Zannier established similar results for totally p-adic numbers and, inspired by work of Ullmo and Zhang, termed this the Bogomolov property. In this paper, we use results on equidistribution of points of low height to generalize both Bogomolov-type results to a wide variety of heights arising in arithmetic dynamics.
LA - eng
KW - Weil height; equidistribution; totally real; totally p-adic; Fekete-Szegő theorem
UR - http://eudml.org/doc/279353
ER -

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.