The density of rational points on non-singular hypersurfaces, I
Timothy Browning
Heath-Brown, Roger
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.*
Wiley-Blackwell
2006
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/215
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>
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