Conference abstracts

Session C6 - Real-Number Complexity

July 18, 18:00 ~ 18:25 - Room B7

Quantitative equidistribution of Galois orbits of points of small height on the $N$-dimensional algebraic torus

Marta Narváez-Clauss

University of Barcelona, Spain   -   martanarvaezclauss@gmail.com

Bilu's equidistribution theorem establishes that, given a strict sequence of points on the $N$-dimensional algebraic torus whose Weil height tends to zero, the Galois orbits of the points are equidistributed with respect to the Haar probability measure of the compact subtorus, $(S^1)^N$. For the case of dimension one, quantitative versions of this result were independently obtained by Petsche and by Favre and Rivera-Letelier.

We present a quantitative version of Bilu's result for the case of any dimension. 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.

As a corollary of our quantitative version for the case of dimension $N$, we give an estimate for the distribution of the solutions of a system of Laurent polynomials with rational coefficients in terms of the size of the coefficients of the polynomials and their degrees.

Joint work with Carlos D'Andrea (Universitat de Barcelona, Spain) and Martín Sombra (Universitat de Barcelona, Spain).

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