Equidistribution of Galois orbits of points of small height

Marta Narvaez Clauss
University of Barcelona
Algebra and Geometry

The roots of the polynomial x^n - 1 lie on the unit circle and determine
the vertices of a regular polygon of n sides. When n grows, these polygons tend to
the circle. In other words, the n-roots of unity converge to the uniform distribution
on S^1 when n tends to in?nity. There are several results that let us extend this
behavior more generally to the case of sequences of ‘small’ algebraic numbers on
a curve. The size of an algebraic number is quanti?ed by its Weil height. In this
talk, I will explain the notion of height and state Bilu’s classical equidistribution
theorem. If time permits, I will present an extension to higher dimension and expose
a quantitative version for this result.

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