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arXiv · 0707.2296

Counting rational points on cubic hypersurfaces

T. D. Browning
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Abstract

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 ε>0, we show that X contains O(B^{D+ε}) rational points of height at most B. The implied constant in this estimate depends upon the choice of εand the coefficients of the cubic form defining X.

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T. D. Browning. 2008-04-16. Counting rational points on cubic hypersurfaces. https://arxiv.org/abs/0707.2296

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