Quantitative equidistribution of Galois orbits of small points in the N-dimensional torus

D’Andrea, Carlos; Narváez-Clauss, Marta; Sombra, Martín

doi:10.2140/ant.2017.11.1627

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Quantitative equidistribution of Galois orbits of small points in the $N$-dimensional torus

Carlos D’Andrea, Marta Narváez-Clauss and Martín Sombra

Vol. 11 (2017), No. 7, 1627–1655

DOI: 10.2140/ant.2017.11.1627

Abstract

We present a quantitative version of Bilu’s theorem on the limit distribution of Galois orbits of sequences of points of small height in the $N$ -dimensional algebraic torus. Our result gives, for a given point, an explicit bound for the discrepancy between its Galois orbit and the uniform distribution on the compact subtorus, in terms of the height and the generalized degree of the point.

Keywords

height of points, algebraic torus, equidistribution of Galois orbits

Mathematical Subject Classification 2010

Primary: 11G50

Secondary: 11K38, 43A25

Milestones

Received: 2 October 2016

Revised: 6 April 2017

Accepted: 23 May 2017

Published: 7 September 2017

Authors

Carlos D’Andrea
Departament de Matemàtiques i Informàtica Universitat de Barcelona Gran Via 585 08007 Barcelona Spain

Marta Narváez-Clauss
Departament de Matemàtiques i Informàtica Universitat de Barcelona Gran Via 585 08007 Barcelona Spain

Martín Sombra
ICREA Passeig Lluís Companys 23 08010 Barcelona Spain Departament de Matemàtiques i Informàtica Universitat de Barcelona Gran Via 585 08007 Barcelona Spain

Vol. 11, No. 7, 2017