{"issue":"4","file":[{"file_id":"14720","success":1,"file_size":724748,"creator":"dernst","relation":"main_file","date_updated":"2024-01-02T07:37:09Z","checksum":"bf29baa9eae8500f3374dbcb80712687","file_name":"2023_QuarterlyJourMath_Horesh.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2024-01-02T07:37:09Z"}],"month":"12","project":[{"name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","license":"https://creativecommons.org/licenses/by/4.0/","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"title":"Equidistribution of primitive lattices in ℝn","volume":74,"oa_version":"Published Version","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"page":"1253-1294","date_published":"2023-12-01T00:00:00Z","type":"journal_article","intvolume":"        74","author":[{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","full_name":"Horesh, Tal","first_name":"Tal","last_name":"Horesh"},{"first_name":"Yakov","full_name":"Karasik, Yakov","last_name":"Karasik"}],"publisher":"Oxford University Press","scopus_import":"1","ddc":["510"],"_id":"14717","doi":"10.1093/qmath/haad008","department":[{"_id":"TiBr"}],"abstract":[{"text":"We count primitive lattices of rank d inside Zn as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subspace that a lattice spans, namely its projection to the Grassmannian; its homothety class and its equivalence class modulo rescaling and rotation, often referred to as a shape. We add to a prior work of Schmidt by allowing sets in the spaces of parameters that are general enough to conclude the joint equidistribution of these parameters. In addition to the primitive d-lattices Λ themselves, we also consider their orthogonal complements in Zn⁠, A1⁠, and show that the equidistribution occurs jointly for Λ and A1⁠. Finally, our asymptotic formulas for the number of primitive lattices include an explicit bound on the error term.","lang":"eng"}],"has_accepted_license":"1","acknowledgement":"This work was done when both authors were visiting Institute of Science and Technology (IST) Austria. T.H. was being supported by Engineering and Physical Sciences Research Council grant EP/P026710/1. Y.K. had a great time there and is grateful for the hospitality. The appendix to this paper is largely based on a mini course T.H. had given at IST in February 2020.","date_updated":"2024-01-02T07:39:55Z","language":[{"iso":"eng"}],"day":"01","year":"2023","publication_status":"published","article_type":"original","quality_controlled":"1","oa":1,"file_date_updated":"2024-01-02T07:37:09Z","external_id":{"arxiv":["2012.04508"]},"publication":"Quarterly Journal of Mathematics","date_created":"2023-12-31T23:01:03Z","status":"public","citation":{"chicago":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>.","short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294.","ama":"Horesh T, Karasik Y. Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. 2023;74(4):1253-1294. doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>","apa":"Horesh, T., &#38; Karasik, Y. (2023). Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>","ieee":"T. Horesh and Y. Karasik, “Equidistribution of primitive lattices in ℝn,” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4. Oxford University Press, pp. 1253–1294, 2023.","ista":"Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 74(4), 1253–1294.","mla":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4, Oxford University Press, 2023, pp. 1253–94, doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>."}}