article published yes Tal Horesh author C8B7BF48-8D81-11E9-BCA9-F536E6697425 Frédéric Paulin author TiBr department Given a place ω of a global function field K over a finite field, with associated affine function ring Rω and completion Kω , the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points (a,b)∈Rω2 in the plane Kω2 , 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 \ZZ2 . https://research-explorer.ista.ac.at/download/12684/12689/2023_JourTheorieNombreBordeaux_Horesh.pdf application/pdfno https://creativecommons.org/licenses/by-nd/4.0/ Université de Bordeaux2022 eng 1246-7405 2118-8572 2001.01534 00092650430000310.5802/JTNB.1222 343679-703 Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 34, no. 3, Université de Bordeaux, 2022, pp. 679–703, doi:<a href="https://doi.org/10.5802/JTNB.1222">10.5802/JTNB.1222</a>. Horesh, T., &#38; Paulin, F. (2022). Effective equidistribution of lattice points in positive characteristic. <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux. <a href="https://doi.org/10.5802/JTNB.1222">https://doi.org/10.5802/JTNB.1222</a> T. Horesh and F. Paulin, “Effective equidistribution of lattice points in positive characteristic,” <i>Journal de Theorie des Nombres de Bordeaux</i>, vol. 34, no. 3. Université de Bordeaux, pp. 679–703, 2022. Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux, 2022. <a href="https://doi.org/10.5802/JTNB.1222">https://doi.org/10.5802/JTNB.1222</a>. Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703. T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022) 679–703. Horesh T, Paulin F. Effective equidistribution of lattice points in positive characteristic. <i>Journal de Theorie des Nombres de Bordeaux</i>. 2022;34(3):679-703. doi:<a href="https://doi.org/10.5802/JTNB.1222">10.5802/JTNB.1222</a> 126842023-02-26T23:01:02Z2025-05-14T11:23:08Z