The Density of Rational Points on Non-Singular Hypersurfaces, I |
| |
Authors: | Browning T D; Heath-Brown D R |
| |
Institution: | School of Mathematics, University of Bristol Bristol BS8 1TW, United Kingdom; t.d.browning{at}bristol.ac.uk
Mathematical Institute 2429 St. Giles', Oxford OX1 3LB, United Kingdom; rhb{at}maths.ox.ac.uk |
| |
Abstract: | For any n 3, let F ZX0, ..., Xn] be a form of degree d 5that defines a non-singular hypersurface X Pn. The main resultin 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 satisfies
, for any > 0. The implied constantin this estimate depends at most upon d, and n. New estimatesare also obtained for the number of representations of a positiveinteger as the sum of three dth powers, and for the paucityof integer solutions to equal sums of like polynomials. 2000Mathematics Subject Classification 11G35 (primary), 11P05, 14G05(secondary). |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|