--- _id: '12684' abstract: - lang: eng 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 . 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." article_processing_charge: No article_type: original author: - first_name: Tal full_name: Horesh, Tal id: C8B7BF48-8D81-11E9-BCA9-F536E6697425 last_name: Horesh - first_name: Frédéric full_name: Paulin, Frédéric last_name: Paulin citation: ama: Horesh T, Paulin F. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 2022;34(3):679-703. doi:10.5802/JTNB.1222 apa: Horesh, T., & Paulin, F. (2022). Effective equidistribution of lattice points in positive characteristic. Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne. https://doi.org/10.5802/JTNB.1222 chicago: Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne, 2022. https://doi.org/10.5802/JTNB.1222. ieee: T. Horesh and F. Paulin, “Effective equidistribution of lattice points in positive characteristic,” Journal de Theorie des Nombres de Bordeaux, vol. 34, no. 3. Centre Mersenne, pp. 679–703, 2022. 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. mla: Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux, vol. 34, no. 3, Centre Mersenne, 2022, pp. 679–703, doi:10.5802/JTNB.1222. short: T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022) 679–703. date_created: 2023-02-26T23:01:02Z date_published: 2022-01-27T00:00:00Z date_updated: 2023-08-04T10:41:40Z day: '27' ddc: - '510' department: - _id: TiBr doi: 10.5802/JTNB.1222 external_id: arxiv: - '2001.01534' isi: - '000926504300003' file: - access_level: open_access checksum: 08f28fded270251f568f610cf5166d69 content_type: application/pdf creator: dernst date_created: 2023-02-27T09:10:13Z date_updated: 2023-02-27T09:10:13Z file_id: '12689' file_name: 2023_JourTheorieNombreBordeaux_Horesh.pdf file_size: 870468 relation: main_file success: 1 file_date_updated: 2023-02-27T09:10:13Z has_accepted_license: '1' intvolume: ' 34' isi: 1 issue: '3' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '01' oa: 1 oa_version: Published Version page: 679-703 publication: Journal de Theorie des Nombres de Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Centre Mersenne quality_controlled: '1' scopus_import: '1' status: public title: Effective equidistribution of lattice points in positive characteristic tmp: image: /image/cc_by_nd.png 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) short: CC BY-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 34 year: '2022' ... --- _id: '6319' abstract: - lang: fre text: Nous étudions le comportement asymptotique du nombre de variétés dans une certaine classe ne satisfaisant pas le principe de Hasse. Cette étude repose sur des résultats récemmentobtenus par Colliot-Thélène. author: - first_name: Régis de la full_name: Bretèche, Régis de la last_name: Bretèche - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: ama: Bretèche R de la, Browning TD. Contre-exemples au principe de Hasse pour certains tores coflasques. Journal de Théorie des Nombres de Bordeaux. 2014;26(1):25-44. doi:10.5802/jtnb.857 apa: Bretèche, R. de la, & Browning, T. D. (2014). Contre-exemples au principe de Hasse pour certains tores coflasques. Journal de Théorie Des Nombres de Bordeaux. Cellule MathDoc/CEDRAM. https://doi.org/10.5802/jtnb.857 chicago: Bretèche, Régis de la, and Timothy D Browning. “Contre-Exemples Au Principe de Hasse Pour Certains Tores Coflasques.” Journal de Théorie Des Nombres de Bordeaux. Cellule MathDoc/CEDRAM, 2014. https://doi.org/10.5802/jtnb.857. ieee: R. de la Bretèche and T. D. Browning, “Contre-exemples au principe de Hasse pour certains tores coflasques,” Journal de Théorie des Nombres de Bordeaux, vol. 26, no. 1. Cellule MathDoc/CEDRAM, pp. 25–44, 2014. ista: Bretèche R de la, Browning TD. 2014. Contre-exemples au principe de Hasse pour certains tores coflasques. Journal de Théorie des Nombres de Bordeaux. 26(1), 25–44. mla: Bretèche, Régis de la, and Timothy D. Browning. “Contre-Exemples Au Principe de Hasse Pour Certains Tores Coflasques.” Journal de Théorie Des Nombres de Bordeaux, vol. 26, no. 1, Cellule MathDoc/CEDRAM, 2014, pp. 25–44, doi:10.5802/jtnb.857. short: R. de la Bretèche, T.D. Browning, Journal de Théorie Des Nombres de Bordeaux 26 (2014) 25–44. date_created: 2019-04-16T13:40:13Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T08:07:03Z doi: 10.5802/jtnb.857 extern: '1' external_id: arxiv: - '1210.4236' intvolume: ' 26' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1210.4236 oa: 1 oa_version: Preprint page: 25-44 publication: Journal de Théorie des Nombres de Bordeaux publication_identifier: issn: - 1246-7405 - 2118-8572 publication_status: published publisher: Cellule MathDoc/CEDRAM quality_controlled: '1' status: public title: Contre-exemples au principe de Hasse pour certains tores coflasques type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2014' ... --- _id: '2904' abstract: - lang: eng 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: fre 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. article_processing_charge: No article_type: original author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819 apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819 chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012. https://doi.org/10.5802/jtnb.819. ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012. ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749. mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819. short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749. date_created: 2018-12-11T12:00:15Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-10-18T07:53:47Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.5802/jtnb.819 file: - access_level: open_access checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67 content_type: application/pdf creator: dernst date_created: 2020-05-11T12:40:39Z date_updated: 2020-07-14T12:45:52Z file_id: '7819' file_name: JTNB_2012__24_3_729_0.pdf file_size: 819275 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' intvolume: ' 24' issue: '3' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 729 - 749 publication: Journal de Theorie des Nombres des Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Université de Bordeaux publist_id: '3843' quality_controlled: '1' scopus_import: '1' status: public title: Weak multipliers for generalized van der Corput sequences type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2012' ...