Vol. 11, No. 7, 2017

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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
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.

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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