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

• Autorzy: Paul Fili , Zachary Miner
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R80: Totally real fields
• 11G50: Heights
• 37P30: Height functions; Green functions; invariant measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 1
• Strony: 15-25

Daty

wydano

2015

Twórcy

autor

Paul Fili

• Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.

autor

Zachary Miner

• Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.

Identyfikatory

DOI

10.4064/aa170-1-2