{"quality_controlled":0,"date_updated":"2019-04-26T07:22:09Z","publication":"Bulletin of the London Mathematical Society","date_created":"2018-12-11T11:45:15Z","citation":{"mla":"Browning, Timothy D., and Roger Heath Brown. “The Density of Rational Points on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*, vol. 38, no. 3, Wiley-Blackwell, 2006, pp. 401–10, doi:10.1112/S0024609305018412.","apa":"Browning, T. D., & Heath Brown, R. (2006). The density of rational points on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*, *38*(3), 401–410. https://doi.org/10.1112/S0024609305018412","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.” *Bulletin of the London Mathematical Society* 38, no. 3 (2006): 401–10. https://doi.org/10.1112/S0024609305018412.","ama":"Browning TD, Heath Brown R. The density of rational points on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*. 2006;38(3):401-410. doi:10.1112/S0024609305018412","ieee":"T. D. Browning and R. Heath Brown, “The density of rational points on non-singular hypersurfaces, I,” *Bulletin of the London Mathematical Society*, vol. 38, no. 3, pp. 401–410, 2006.","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."},"abstract":[{"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 > 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.*","lang":"eng"}],"year":"2006","_id":"215","publisher":"Wiley-Blackwell","publication_status":"published","author":[{"full_name":"Timothy Browning","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"full_name":"Heath-Brown, Roger","last_name":"Heath Brown","first_name":"Roger"}],"doi":"10.1112/S0024609305018412","volume":38,"type":"journal_article","day":"23","title":"The density of rational points on non-singular hypersurfaces, I","publist_id":"7697","date_published":"2006-12-23T00:00:00Z","issue":"3","extern":1,"month":"12","page":"401 - 410","status":"public","intvolume":" 38"}