{"abstract":[{"lang":"eng","text":"An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points."}],"main_file_link":[{"url":"https://arxiv.org/abs/1705.01999","open_access":"1"}],"department":[{"_id":"TiBr"}],"issue":"8","publication_status":"published","date_published":"2019-04-15T00:00:00Z","date_updated":"2023-08-24T14:34:56Z","month":"04","article_processing_charge":"No","day":"15","type":"journal_article","status":"public","title":"Sieving rational points on varieties","quality_controlled":"1","scopus_import":"1","publisher":"American Mathematical Society","date_created":"2018-12-11T11:45:01Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","oa":1,"_id":"175","language":[{"iso":"eng"}],"citation":{"short":"T.D. Browning, D. Loughran, Transactions of the American Mathematical Society 371 (2019) 5757–5785.","ama":"Browning TD, Loughran D. Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. 2019;371(8):5757-5785. doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>","chicago":"Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>.","ista":"Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785.","apa":"Browning, T. D., &#38; Loughran, D. (2019). Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>","ieee":"T. D. Browning and D. Loughran, “Sieving rational points on varieties,” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8. American Mathematical Society, pp. 5757–5785, 2019.","mla":"Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8, American Mathematical Society, 2019, pp. 5757–85, doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>."},"publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"external_id":{"isi":["000464034200019"],"arxiv":["1705.01999"]},"publication":"Transactions of the American Mathematical Society","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Daniel","last_name":"Loughran","full_name":"Loughran, Daniel"}],"page":"5757-5785","doi":"10.1090/tran/7514","isi":1,"year":"2019","publist_id":"7746","volume":371,"intvolume":"       371"}