{"publisher":"Presses Universitaires de Franche-Comté","project":[{"name":"Between rational and integral points","grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425"}],"publication":"Publications mathématiques de Besançon - Algèbre et Théorie des nombres","month":"06","page":"85-107","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":2023,"_id":"18179","date_created":"2024-10-06T22:01:13Z","article_processing_charge":"Yes (in subscription journal)","date_published":"2023-06-15T00:00:00Z","corr_author":"1","day":"15","department":[{"_id":"TiBr"}],"file_date_updated":"2024-10-07T11:32:32Z","date_updated":"2024-10-07T11:34:56Z","publication_identifier":{"eissn":["2592-6616"],"issn":["2804-8504"]},"author":[{"first_name":"Antonin","full_name":"Guilloux, Antonin","last_name":"Guilloux"},{"last_name":"Horesh","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal","full_name":"Horesh, Tal"}],"year":"2023","oa":1,"quality_controlled":"1","ddc":["510"],"license":"https://creativecommons.org/licenses/by-nd/4.0/","acknowledgement":"The second author is supported by EPRSC grant EP/P026710/1.","title":"p-adic directions of primitive vectors","abstract":[{"lang":"eng","text":"Linnik type problems concern the distribution of projections of integral points on the unit sphere as their norm increases, and different generalizations of this phenomenon. Our work addresses a question of this type: we prove the uniform distribution of the projections of primitive Z2 points in the p-adic unit sphere, as their (real) norm tends to infinity. The proof is via counting lattice points in semi-simple S-arithmetic groups."},{"text":"Les problèmes de type Linnik concernent la distribution des projections des points entiers sur la sphère unitaire lorsque leur norme augmente et différentes généralisations de ce phénomène. Notre travail s’intéresse à une question de ce type : nous prouvons la distribution uniforme des projections des points primitifs de Z2 sur la sphère unitaire p-adique lorsque leur norme (réelle) tend vers l’infini. La preuve se fait en comptant les points d’un réseau dans des S-groupes arithmétiques semi-simples.","lang":"fre"}],"file":[{"file_name":"2023_MathBesancon_Guilloux.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","checksum":"cefc47a2cf55a87f8e4960197f73353b","file_size":1399390,"success":1,"file_id":"18186","relation":"main_file","date_updated":"2024-10-07T11:32:32Z","date_created":"2024-10-07T11:32:32Z"}],"status":"public","oa_version":"Published Version","scopus_import":"1","article_type":"original","doi":"10.5802/pmb.50","citation":{"apa":"Guilloux, A., &#38; Horesh, T. (2023). p-adic directions of primitive vectors. <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>. Presses Universitaires de Franche-Comté. <a href=\"https://doi.org/10.5802/pmb.50\">https://doi.org/10.5802/pmb.50</a>","mla":"Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.” <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>, vol. 2023, Presses Universitaires de Franche-Comté, 2023, pp. 85–107, doi:<a href=\"https://doi.org/10.5802/pmb.50\">10.5802/pmb.50</a>.","ieee":"A. Guilloux and T. Horesh, “p-adic directions of primitive vectors,” <i>Publications mathématiques de Besançon - Algèbre et Théorie des nombres</i>, vol. 2023. Presses Universitaires de Franche-Comté, pp. 85–107, 2023.","ista":"Guilloux A, Horesh T. 2023. p-adic directions of primitive vectors. Publications mathématiques de Besançon - Algèbre et Théorie des nombres. 2023, 85–107.","ama":"Guilloux A, Horesh T. p-adic directions of primitive vectors. <i>Publications mathématiques de Besançon - Algèbre et Théorie des nombres</i>. 2023;2023:85-107. doi:<a href=\"https://doi.org/10.5802/pmb.50\">10.5802/pmb.50</a>","short":"A. Guilloux, T. Horesh, Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres 2023 (2023) 85–107.","chicago":"Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.” <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>. Presses Universitaires de Franche-Comté, 2023. <a href=\"https://doi.org/10.5802/pmb.50\">https://doi.org/10.5802/pmb.50</a>."},"publication_status":"published","has_accepted_license":"1","language":[{"iso":"eng"}],"tmp":{"short":"CC BY-ND (4.0)","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png"},"intvolume":"      2023","type":"journal_article","external_id":{"arxiv":["2103.10889"]}}