[{"year":"2022","quality_controlled":"1","abstract":[{"text":"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 .","lang":"eng"}],"date_updated":"2025-05-14T11:23:08Z","page":"679-703","date_published":"2022-01-27T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-02-26T23:01:02Z","citation":{"ieee":"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.","ama":"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>","chicago":"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>.","apa":"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>","short":"T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022) 679–703.","mla":"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>.","ista":"Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703."},"doi":"10.5802/JTNB.1222","language":[{"iso":"eng"}],"isi":1,"has_accepted_license":"1","type":"journal_article","publisher":"Université de Bordeaux","oa_version":"Published Version","issue":"3","title":"Effective equidistribution of lattice points in positive characteristic","file_date_updated":"2023-02-27T09:10:13Z","month":"01","corr_author":"1","_id":"12684","volume":34,"license":"https://creativecommons.org/licenses/by-nd/4.0/","department":[{"_id":"TiBr"}],"publication_status":"published","arxiv":1,"intvolume":"        34","oa":1,"day":"27","external_id":{"isi":["000926504300003"],"arxiv":["2001.01534"]},"publication":"Journal de Theorie des Nombres de Bordeaux","article_processing_charge":"No","ddc":["510"],"acknowledgement":"The authors warmly thank Amos Nevo for having presented the authors to each other during\r\na beautiful conference in Goa in February 2016, where the idea of this paper was born. The\r\nfirst author thanks the IHES for two post-doctoral years when most of this paper was discussed,\r\nand the Topology team in Orsay for financial support at the final stage. The first author was\r\nsupported by the EPRSC EP/P026710/1 grant. Finally, we warmly thank the referee for many\r\nvery helpful comments that have improved the readability of this paper.","author":[{"first_name":"Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","full_name":"Horesh, Tal","last_name":"Horesh"},{"first_name":"Frédéric","last_name":"Paulin","full_name":"Paulin, Frédéric"}],"publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"article_type":"original","file":[{"access_level":"open_access","content_type":"application/pdf","file_size":870468,"date_created":"2023-02-27T09:10:13Z","file_name":"2023_JourTheorieNombreBordeaux_Horesh.pdf","file_id":"12689","checksum":"08f28fded270251f568f610cf5166d69","creator":"dernst","success":1,"date_updated":"2023-02-27T09:10:13Z","relation":"main_file"}]}]