[{"page":"920-940","external_id":{"isi":["000468857300025"],"arxiv":["1810.08426"]},"file":[{"date_created":"2019-04-16T09:12:20Z","relation":"main_file","file_size":379158,"creator":"tbrownin","content_type":"application/pdf","file_id":"6311","date_updated":"2020-07-14T12:47:27Z","access_level":"open_access","checksum":"a63594a3a91b4ba6e2a1b78b0720b3d0","file_name":"wliqun.pdf"}],"date_published":"2019-06-20T00:00:00Z","arxiv":1,"scopus_import":"1","publication_identifier":{"eissn":["10902082"],"issn":["00018708"]},"day":"20","oa_version":"Submitted Version","type":"journal_article","date_updated":"2023-08-25T10:11:55Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"TiBr"}],"doi":"10.1016/j.aim.2019.04.031","language":[{"iso":"eng"}],"publisher":"Elsevier","file_date_updated":"2020-07-14T12:47:27Z","volume":349,"status":"public","month":"06","date_created":"2019-04-16T09:13:25Z","isi":1,"intvolume":"       349","year":"2019","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Hu","first_name":"L.Q.","full_name":"Hu, L.Q."}],"quality_controlled":"1","citation":{"mla":"Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>, vol. 349, Elsevier, 2019, pp. 920–40, doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>.","apa":"Browning, T. D., &#38; Hu, L. Q. (2019). Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>","ista":"Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940.","short":"T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.","chicago":"Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>.","ama":"Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. 2019;349:920-940. doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>","ieee":"T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” <i>Advances in Mathematics</i>, vol. 349. Elsevier, pp. 920–940, 2019."},"abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy–Littlewood circle method."}],"publication_status":"published","_id":"6310","oa":1,"ddc":["512"],"title":"Counting rational points on biquadratic hypersurfaces","publication":"Advances in Mathematics"},{"publisher":"Academic Press","volume":308,"status":"public","month":"02","date_created":"2018-12-11T11:50:34Z","isi":1,"publist_id":"6173","intvolume":"       308","year":"2017","quality_controlled":"1","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Bárány","first_name":"Imre","full_name":"Bárány, Imre"},{"full_name":"Robins, Sinai","first_name":"Sinai","last_name":"Robins"}],"citation":{"ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” <i>Advances in Mathematics</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">https://doi.org/10.1016/j.aim.2016.12.026</a>.","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. <i>Advances in Mathematics</i>. 2017;308:627-644. doi:<a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">10.1016/j.aim.2016.12.026</a>","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” <i>Advances in Mathematics</i>, vol. 308. Academic Press, pp. 627–644, 2017.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” <i>Advances in Mathematics</i>, vol. 308, Academic Press, 2017, pp. 627–44, doi:<a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">10.1016/j.aim.2016.12.026</a>.","apa":"Akopyan, A., Bárány, I., &#38; Robins, S. (2017). Algebraic vertices of non-convex polyhedra. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">https://doi.org/10.1016/j.aim.2016.12.026</a>"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"publication_status":"published","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"_id":"1180","oa":1,"publication":"Advances in Mathematics","title":"Algebraic vertices of non-convex polyhedra","page":"627 - 644","external_id":{"isi":["000409292900015"]},"date_published":"2017-02-21T00:00:00Z","scopus_import":"1","publication_identifier":{"issn":["00018708"]},"day":"21","oa_version":"Submitted Version","type":"journal_article","date_updated":"2023-09-20T11:21:27Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2016.12.026","ec_funded":1}]