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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2001.01534 |
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Table of Contents:
- Given a place $ω$ of a global function field $K$ over a finite field, with associated affine function ring $R_ω$ and completion $K_ω$, the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points $(a,b)\in {R_ω}^2$ in the plane ${K_ω}^2$, 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 $\ZZ^2$.