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