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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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| _version_ | 1866915583618973696 |
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| author | Horesh, Tal Paulin, Frédéric |
| author_facet | Horesh, Tal Paulin, Frédéric |
| 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 $\ZZ^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_01534 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Effective equidistribution of lattice points in positive characteristic Horesh, Tal Paulin, Frédéric Number Theory 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 $\ZZ^2$. |
| title | Effective equidistribution of lattice points in positive characteristic |
| topic | Number Theory |
| url | https://arxiv.org/abs/2001.01534 |