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The density of rational points on non-singular hypersurfaces, II |
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| Authors: | Browning T D; Heath-Brown D R; Starr J M |
| Institution: | School of Mathematics, Bristol University Bristol, BS8 1TW, United Kingdom; e-mail: t.d.browning{at}bristol.ac.uk Mathematical Institute 24–29 St. Giles', Oxford, OX1 3LB, United Kingdom; e-mail: rhb{at}maths.ox.ac.uk Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA; e-mail: jstarr{at}math.mit.edu |
| Abstract: | For any integers d,n  2, let X  Pn be a non-singular hypersurfaceof degree d that is defined over the rational numbers. The mainresult in this paper is a proof that the number of rationalpoints on X which have height at most B is O(Bn – 1 + ), for any > 0. The implied constant in this estimate dependsat most upon d, and n. 2000 Mathematics Subject Classification11D45 (primary), 11G35, 14G05 (secondary). |
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