[{"arxiv":1,"doi":"10.5802/JTNB.1222","day":"27","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":"2023-08-04T10:41:40Z","citation":{"apa":"Horesh, T., &#38; Paulin, F. (2022). Effective equidistribution of lattice points in positive characteristic. <i>Journal de Theorie Des Nombres de Bordeaux</i>. Centre Mersenne. <a href=\"https://doi.org/10.5802/JTNB.1222\">https://doi.org/10.5802/JTNB.1222</a>","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>","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. Centre Mersenne, pp. 679–703, 2022.","chicago":"Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” <i>Journal de Theorie Des Nombres de Bordeaux</i>. Centre Mersenne, 2022. <a href=\"https://doi.org/10.5802/JTNB.1222\">https://doi.org/10.5802/JTNB.1222</a>.","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, Centre Mersenne, 2022, pp. 679–703, doi:<a href=\"https://doi.org/10.5802/JTNB.1222\">10.5802/JTNB.1222</a>.","short":"T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022) 679–703.","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."},"year":"2022","isi":1,"external_id":{"isi":["000926504300003"],"arxiv":["2001.01534"]},"volume":34,"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.","ddc":["510"],"publication_status":"published","department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2023-02-26T23:01:02Z","title":"Effective equidistribution of lattice points in positive characteristic","intvolume":"        34","_id":"12684","scopus_import":"1","license":"https://creativecommons.org/licenses/by-nd/4.0/","author":[{"first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"full_name":"Paulin, Frédéric","last_name":"Paulin","first_name":"Frédéric"}],"issue":"3","publisher":"Centre Mersenne","article_type":"original","page":"679-703","quality_controlled":"1","file_date_updated":"2023-02-27T09:10:13Z","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"date_published":"2022-01-27T00:00:00Z","type":"journal_article","file":[{"file_name":"2023_JourTheorieNombreBordeaux_Horesh.pdf","content_type":"application/pdf","date_updated":"2023-02-27T09:10:13Z","checksum":"08f28fded270251f568f610cf5166d69","file_size":870468,"date_created":"2023-02-27T09:10:13Z","creator":"dernst","file_id":"12689","success":1,"access_level":"open_access","relation":"main_file"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","oa_version":"Published Version","month":"01","publication":"Journal de Theorie des Nombres de Bordeaux","has_accepted_license":"1","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Journal de Theorie des Nombres des Bordeaux","oa_version":"Published Version","month":"01","file":[{"date_updated":"2020-07-14T12:45:52Z","content_type":"application/pdf","file_name":"JTNB_2012__24_3_729_0.pdf","date_created":"2020-05-11T12:40:39Z","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","file_size":819275,"file_id":"7819","creator":"dernst","access_level":"open_access","relation":"main_file"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_published":"2012-01-01T00:00:00Z","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"publist_id":"3843","oa":1,"quality_controlled":"1","page":"729 - 749","file_date_updated":"2020-07-14T12:45:52Z","publisher":"Université de Bordeaux","article_type":"original","scopus_import":"1","_id":"2904","issue":"3","author":[{"first_name":"Florian","last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T12:00:15Z","article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication_status":"published","intvolume":"        24","title":"Weak multipliers for generalized van der Corput sequences","volume":24,"ddc":["510"],"year":"2012","citation":{"chicago":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux, 2012. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>.","ieee":"F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” <i>Journal de Theorie des Nombres des Bordeaux</i>, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012.","ama":"Pausinger F. Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie des Nombres des Bordeaux</i>. 2012;24(3):729-749. doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>","apa":"Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>","ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.","mla":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>."},"date_updated":"2023-10-18T07:53:47Z","day":"01","doi":"10.5802/jtnb.819","abstract":[{"text":"Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.","lang":"eng"},{"text":"Les suites de Van der Corput généralisées sont dessuites unidimensionnelles et infinies dans l’intervalle de l’unité.Elles sont générées par permutations des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de distribution uniforme des suites de Halton nous nousintéressons aux permutations de la formuleP(i)  =ai(modb)pour les entiers premiers entre euxaetb. Dans cet article nousidentifions des multiplicateursagénérant des suites de Van derCorput ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée.","lang":"fre"}]}]