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arXiv · 2001.01534

Effective equidistribution of lattice points in positive characteristic

Tal Horesh·Frédéric Paulin
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Abstract

Given a place $\omega$ of a global function field $K$ over a finite field, with associated affine function ring $R_\omega$ and completion $K_\omega$, the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points $(a,b)\in {R_\omega}^2$ in the plane ${K_\omega}^2$, and for renormalized solutions to the gcd equation $ax+by=1$. The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in $\ZZ^2$.

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Tal Horesh, Frédéric Paulin. 2020-01-06. Effective equidistribution of lattice points in positive characteristic. https://arxiv.org/abs/2001.01534

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