--- _id: '6310' 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. article_processing_charge: No author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: L.Q. full_name: Hu, L.Q. last_name: Hu citation: ama: Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 2019;349:920-940. doi:10.1016/j.aim.2019.04.031 apa: Browning, T. D., & Hu, L. Q. (2019). Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2019.04.031 chicago: Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” Advances in Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.aim.2019.04.031. ieee: T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” Advances in Mathematics, vol. 349. Elsevier, pp. 920–940, 2019. ista: Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940. mla: Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” Advances in Mathematics, vol. 349, Elsevier, 2019, pp. 920–40, doi:10.1016/j.aim.2019.04.031. short: T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940. date_created: 2019-04-16T09:13:25Z date_published: 2019-06-20T00:00:00Z date_updated: 2023-08-25T10:11:55Z day: '20' ddc: - '512' department: - _id: TiBr doi: 10.1016/j.aim.2019.04.031 external_id: arxiv: - '1810.08426' isi: - '000468857300025' file: - access_level: open_access checksum: a63594a3a91b4ba6e2a1b78b0720b3d0 content_type: application/pdf creator: tbrownin date_created: 2019-04-16T09:12:20Z date_updated: 2020-07-14T12:47:27Z file_id: '6311' file_name: wliqun.pdf file_size: 379158 relation: main_file file_date_updated: 2020-07-14T12:47:27Z has_accepted_license: '1' intvolume: ' 349' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 920-940 publication: Advances in Mathematics publication_identifier: eissn: - '10902082' issn: - '00018708' publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Counting rational points on biquadratic hypersurfaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 349 year: '2019' ... --- _id: '1180' 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. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Imre full_name: Bárány, Imre last_name: Bárány - first_name: Sinai full_name: Robins, Sinai last_name: Robins citation: ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026 apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026 chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026. ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017. ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644. mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026. short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644. date_created: 2018-12-11T11:50:34Z date_published: 2017-02-21T00:00:00Z date_updated: 2023-09-20T11:21:27Z day: '21' department: - _id: HeEd doi: 10.1016/j.aim.2016.12.026 ec_funded: 1 external_id: isi: - '000409292900015' intvolume: ' 308' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1508.07594 month: '02' oa: 1 oa_version: Submitted Version page: 627 - 644 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Advances in Mathematics publication_identifier: issn: - '00018708' publication_status: published publisher: Academic Press publist_id: '6173' quality_controlled: '1' scopus_import: '1' status: public title: Algebraic vertices of non-convex polyhedra type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 308 year: '2017' ...