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