[{"language":[{"iso":"eng"}],"oa_version":"Preprint","month":"12","publication":"Science China Mathematics","main_file_link":[{"url":"https://arxiv.org/abs/1709.09476","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["16747283"]},"oa":1,"date_published":"2019-12-01T00:00:00Z","type":"journal_article","publisher":"Springer","article_type":"original","page":"2435–2446","quality_controlled":"1","publication_status":"published","article_processing_charge":"No","date_created":"2019-07-07T21:59:25Z","department":[{"_id":"TiBr"}],"title":"On a certain non-split cubic surface","intvolume":"        62","_id":"6620","scopus_import":"1","author":[{"full_name":"De La Bretèche, Régis","last_name":"De La Bretèche","first_name":"Régis"},{"last_name":"Destagnol","first_name":"Kevin N","full_name":"Destagnol, Kevin N","id":"44DDECBC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jianya","last_name":"Liu","full_name":"Liu, Jianya"},{"full_name":"Wu, Jie","first_name":"Jie","last_name":"Wu"},{"full_name":"Zhao, Yongqiang","last_name":"Zhao","first_name":"Yongqiang"}],"issue":"12","volume":62,"doi":"10.1007/s11425-018-9543-8","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of ℙ3ℚ given by the following equation 𝑥0(𝑥21+𝑥22)−𝑥33=0 in agreement with the Manin-Peyre conjectures.\r\n"}],"date_updated":"2023-08-28T12:32:20Z","citation":{"mla":"De La Bretèche, Régis, et al. “On a Certain Non-Split Cubic Surface.” <i>Science China Mathematics</i>, vol. 62, no. 12, Springer, 2019, pp. 2435–2446, doi:<a href=\"https://doi.org/10.1007/s11425-018-9543-8\">10.1007/s11425-018-9543-8</a>.","short":"R. De La Bretèche, K.N. Destagnol, J. Liu, J. Wu, Y. Zhao, Science China Mathematics 62 (2019) 2435–2446.","ista":"De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. 2019. On a certain non-split cubic surface. Science China Mathematics. 62(12), 2435–2446.","ama":"De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. On a certain non-split cubic surface. <i>Science China Mathematics</i>. 2019;62(12):2435–2446. doi:<a href=\"https://doi.org/10.1007/s11425-018-9543-8\">10.1007/s11425-018-9543-8</a>","apa":"De La Bretèche, R., Destagnol, K. N., Liu, J., Wu, J., &#38; Zhao, Y. (2019). On a certain non-split cubic surface. <i>Science China Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11425-018-9543-8\">https://doi.org/10.1007/s11425-018-9543-8</a>","chicago":"De La Bretèche, Régis, Kevin N Destagnol, Jianya Liu, Jie Wu, and Yongqiang Zhao. “On a Certain Non-Split Cubic Surface.” <i>Science China Mathematics</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s11425-018-9543-8\">https://doi.org/10.1007/s11425-018-9543-8</a>.","ieee":"R. De La Bretèche, K. N. Destagnol, J. Liu, J. Wu, and Y. Zhao, “On a certain non-split cubic surface,” <i>Science China Mathematics</i>, vol. 62, no. 12. Springer, pp. 2435–2446, 2019."},"year":"2019","isi":1,"external_id":{"isi":["000509102200001"],"arxiv":["1709.09476"]}},{"quality_controlled":"1","publisher":"Elsevier","article_type":"original","_id":"6835","scopus_import":"1","author":[{"id":"44DDECBC-F248-11E8-B48F-1D18A9856A87","last_name":"Destagnol","first_name":"Kevin N","full_name":"Destagnol, Kevin N"},{"last_name":"Sofos","first_name":"Efthymios","full_name":"Sofos, Efthymios"}],"issue":"11","publication_status":"published","article_processing_charge":"No","department":[{"_id":"TiBr"}],"date_created":"2019-09-01T22:00:55Z","title":"Rational points and prime values of polynomials in moderately many variables","intvolume":"       156","volume":156,"date_updated":"2023-08-29T07:18:02Z","year":"2019","citation":{"ista":"Destagnol KN, Sofos E. 2019. Rational points and prime values of polynomials in moderately many variables. Bulletin des Sciences Mathematiques. 156(11), 102794.","short":"K.N. Destagnol, E. Sofos, Bulletin Des Sciences Mathematiques 156 (2019).","mla":"Destagnol, Kevin N., and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 156, no. 11, 102794, Elsevier, 2019, doi:<a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">10.1016/j.bulsci.2019.102794</a>.","ieee":"K. N. Destagnol and E. Sofos, “Rational points and prime values of polynomials in moderately many variables,” <i>Bulletin des Sciences Mathematiques</i>, vol. 156, no. 11. Elsevier, 2019.","chicago":"Destagnol, Kevin N, and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">https://doi.org/10.1016/j.bulsci.2019.102794</a>.","apa":"Destagnol, K. N., &#38; Sofos, E. (2019). Rational points and prime values of polynomials in moderately many variables. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">https://doi.org/10.1016/j.bulsci.2019.102794</a>","ama":"Destagnol KN, Sofos E. Rational points and prime values of polynomials in moderately many variables. <i>Bulletin des Sciences Mathematiques</i>. 2019;156(11). doi:<a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">10.1016/j.bulsci.2019.102794</a>"},"isi":1,"external_id":{"arxiv":["1801.03082"],"isi":["000496342100002"]},"doi":"10.1016/j.bulsci.2019.102794","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"We derive the Hasse principle and weak approximation for fibrations of certain varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our varieties are defined through polynomials in many variables and part of our work is devoted to establishing Schinzel's hypothesis for polynomials of this kind. This last part is achieved by using arguments behind Birch's well-known result regarding the Hasse principle for complete intersections with the notable difference that we prove our result in 50% fewer variables than in the classical Birch setting. We also study the problem of square-free values of an integer polynomial with 66.6% fewer variables than in the Birch setting."}],"language":[{"iso":"eng"}],"publication":"Bulletin des Sciences Mathematiques","oa_version":"Preprint","month":"11","article_number":"102794","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.03082"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2019-11-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0007-4497"]},"oa":1}]