[{"publication_status":"published","oa":1,"file_date_updated":"2024-01-02T07:37:09Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":74,"arxiv":1,"article_processing_charge":"Yes (via OA deal)","issue":"4","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"14720","success":1,"date_created":"2024-01-02T07:37:09Z","file_name":"2023_QuarterlyJourMath_Horesh.pdf","creator":"dernst","file_size":724748,"date_updated":"2024-01-02T07:37:09Z","access_level":"open_access","checksum":"bf29baa9eae8500f3374dbcb80712687"}],"_id":"14717","date_published":"2023-12-01T00:00:00Z","abstract":[{"lang":"eng","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."}],"external_id":{"arxiv":["2012.04508"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-01-02T07:39:55Z","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"article_type":"original","year":"2023","has_accepted_license":"1","oa_version":"Published Version","publisher":"Oxford University Press","publication":"Quarterly Journal of Mathematics","quality_controlled":"1","department":[{"_id":"TiBr"}],"intvolume":"        74","status":"public","page":"1253-1294","month":"12","date_created":"2023-12-31T23:01:03Z","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"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.","language":[{"iso":"eng"}],"doi":"10.1093/qmath/haad008","ddc":["510"],"citation":{"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>.","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>.","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.","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>","short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294."},"title":"Equidistribution of primitive lattices in ℝn","day":"01","type":"journal_article","author":[{"first_name":"Tal","full_name":"Horesh, Tal","last_name":"Horesh","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"first_name":"Yakov","full_name":"Karasik, Yakov","last_name":"Karasik"}]}]