{"day":"23","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Roger","last_name":"Heath Brown","full_name":"Heath-Brown, Roger"}],"type":"journal_article","month":"12","extern":1,"_id":"215","publication_status":"published","date_created":"2018-12-11T11:45:15Z","publication":"Bulletin of the London Mathematical Society","title":"The density of rational points on non-singular hypersurfaces, I","doi":"10.1112/S0024609305018412","publist_id":"7697","status":"public","year":"2006","intvolume":"        38","date_updated":"2021-01-12T06:55:36Z","publisher":"Wiley-Blackwell","issue":"3","abstract":[{"lang":"eng","text":"For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε &gt; 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained for the number of representations of a positive integer as the sum of three dth powers, and for the paucity of integer solutions to equal sums of like polynomials.*"}],"quality_controlled":0,"date_published":"2006-12-23T00:00:00Z","page":"401 - 410","citation":{"apa":"Browning, T. D., &#38; Heath Brown, R. (2006). The density of rational points on non-singular hypersurfaces, I. <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1112/S0024609305018412\">https://doi.org/10.1112/S0024609305018412</a>","mla":"Browning, Timothy D., and Roger Heath Brown. “The Density of Rational Points on Non-Singular Hypersurfaces, I.” <i>Bulletin of the London Mathematical Society</i>, vol. 38, no. 3, Wiley-Blackwell, 2006, pp. 401–10, doi:<a href=\"https://doi.org/10.1112/S0024609305018412\">10.1112/S0024609305018412</a>.","ieee":"T. D. Browning and R. Heath Brown, “The density of rational points on non-singular hypersurfaces, I,” <i>Bulletin of the London Mathematical Society</i>, vol. 38, no. 3. Wiley-Blackwell, pp. 401–410, 2006.","short":"T.D. Browning, R. Heath Brown, Bulletin of the London Mathematical Society 38 (2006) 401–410.","chicago":"Browning, Timothy D, and Roger Heath Brown. “The Density of Rational Points on Non-Singular Hypersurfaces, I.” <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell, 2006. <a href=\"https://doi.org/10.1112/S0024609305018412\">https://doi.org/10.1112/S0024609305018412</a>.","ista":"Browning TD, Heath Brown R. 2006. The density of rational points on non-singular hypersurfaces, I. Bulletin of the London Mathematical Society. 38(3), 401–410.","ama":"Browning TD, Heath Brown R. The density of rational points on non-singular hypersurfaces, I. <i>Bulletin of the London Mathematical Society</i>. 2006;38(3):401-410. doi:<a href=\"https://doi.org/10.1112/S0024609305018412\">10.1112/S0024609305018412</a>"},"volume":38}