Counting rational points on cubic hypersurfaces

Details Counting rational points on cubic hypersurfaces Counting rational points on cubic hypersurfaces

2007-07-16

arxiv.org/abs/0707.2296v2

Mathematics

Number Theory

19 pages

Scientific paper

Let X be a geometrically integral projective cubic hypersurface defined over
the rationals, with dimension D and singular locus of dimension at most D-4.
For any \epsilon>0, we show that X contains O(B^{D+\epsilon}) rational points
of height at most B. The implied constant in this estimate depends upon the
choice of \epsilon and the coefficients of the cubic form defining X.

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