{"abstract":[{"text":"We give an upper bound for the number of rational points of height at most B, lying on a surface defined by a quadratic form Q. The bound shows an explicit dependence on Q. It is optimal with respect to B, and is also optimal for typical forms Q.","lang":"eng"}],"publisher":"Alliance of Diamond Open Access Journals","article_processing_charge":"No","language":[{"iso":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","doi":"10.19086/da.4375","citation":{"chicago":"Browning, Timothy D, and Roger Heath-Brown. “Counting Rational Points on Quadric Surfaces.” <i>Discrete Analysis</i>. Alliance of Diamond Open Access Journals, 2018. <a href=\"https://doi.org/10.19086/da.4375\">https://doi.org/10.19086/da.4375</a>.","ieee":"T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,” <i>Discrete Analysis</i>, vol. 15. Alliance of Diamond Open Access Journals, pp. 1–29, 2018.","ama":"Browning TD, Heath-Brown R. Counting rational points on quadric surfaces. <i>Discrete Analysis</i>. 2018;15:1-29. doi:<a href=\"https://doi.org/10.19086/da.4375\">10.19086/da.4375</a>","ista":"Browning TD, Heath-Brown R. 2018. Counting rational points on quadric surfaces. Discrete Analysis. 15, 1–29.","mla":"Browning, Timothy D., and Roger Heath-Brown. “Counting Rational Points on Quadric Surfaces.” <i>Discrete Analysis</i>, vol. 15, Alliance of Diamond Open Access Journals, 2018, pp. 1–29, doi:<a href=\"https://doi.org/10.19086/da.4375\">10.19086/da.4375</a>.","apa":"Browning, T. D., &#38; Heath-Brown, R. (2018). Counting rational points on quadric surfaces. <i>Discrete Analysis</i>. Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/da.4375\">https://doi.org/10.19086/da.4375</a>","short":"T.D. Browning, R. Heath-Brown, Discrete Analysis 15 (2018) 1–29."},"day":"07","status":"public","date_published":"2018-09-07T00:00:00Z","publication_identifier":{"eissn":["2397-3129"]},"main_file_link":[{"url":"https://arxiv.org/abs/1801.00979","open_access":"1"}],"quality_controlled":"1","external_id":{"arxiv":["1801.00979"]},"publication":"Discrete Analysis","extern":"1","intvolume":"        15","tmp":{"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","image":"/images/cc_by.png"},"oa_version":"Preprint","oa":1,"publication_status":"published","type":"journal_article","year":"2018","author":[{"last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"last_name":"Heath-Brown","full_name":"Heath-Brown, Roger","first_name":"Roger"}],"ddc":["512"],"_id":"178","title":"Counting rational points on quadric surfaces","date_created":"2018-12-11T11:45:02Z","date_updated":"2022-08-26T09:13:02Z","page":"1 - 29","month":"09","volume":15}