Geodesic
Equidistribution and the heights of totally real and totally $p$-adic numbers
Paul Fili 1   ; Zachary Miner 2
1 Department of Mathematics Oklahoma State University Stillwater, OK 74078, U.S.A.
2 Department of Mathematics University of Texas at Austin Austin, TX 78712, U.S.A.
Acta Arithmetica, Tome 170 (2015) no. 1, pp. 15-25 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/aa170-1-2
Keywords: smyth among first study spectrum weil height field totally real numbers establishing lower upper bounds limit infimum height totally real integers determining isolated values height later bombieri zannier established similar results totally p adic numbers inspired work ullmo zhang termed bogomolov property paper results equidistribution points low height generalize bogomolov type results wide variety heights arising arithmetic dynamics

Paul Fili  1   ; Zachary Miner  2

1 Department of Mathematics Oklahoma State University Stillwater, OK 74078, U.S.A.
2 Department of Mathematics University of Texas at Austin Austin, TX 78712, U.S.A. 
@article{10_4064_aa170_1_2,
     author = {Paul Fili and Zachary Miner},
     title = {Equidistribution and the heights of
 totally real and totally $p$-adic numbers},
     journal = {Acta Arithmetica},
     pages = {15--25},
     year = {2015},
     volume = {170},
     number = {1},
     doi = {10.4064/aa170-1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa170-1-2/}
}
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
SP  - 15
EP  - 25
VL  - 170
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa170-1-2/
DO  - 10.4064/aa170-1-2
LA  - en
ID  - 10_4064_aa170_1_2
ER  - 
%0 Journal Article
%A Paul Fili
%A Zachary Miner
%T Equidistribution and the heights of
 totally real and totally $p$-adic numbers
%J Acta Arithmetica
%D 2015
%P 15-25
%V 170
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/aa170-1-2/
%R 10.4064/aa170-1-2
%G en
%F 10_4064_aa170_1_2
Paul Fili; Zachary Miner. Equidistribution and the heights of
 totally real and totally $p$-adic numbers. Acta Arithmetica, Tome 170 (2015) no. 1, pp. 15-25. doi: 10.4064/aa170-1-2

Cité par Sources :