• Corpus ID: 102341507

# Rational points of bounded height on threefolds

@inproceedings{Salberger2007RationalPO,
title={Rational points of bounded height on threefolds},
author={Per Salberger},
year={2007}
}
Let ne,f (B) be the number of non-trivial positive integer solutions x0, x1, x2, y0, y1, y2 ≤ B to the simultaneous equations x0 + x e 1 + x e 2 = y e 0 + y e 1 + y e 2, x f 0 + x f 1 + x f 2 = y f 0 + y f 1 + y f 2 . We show that n1,4(B) = Oe(B), n1,5(B) = Oe(B) and that ne,f (B) = Oe,f,e(B 5/2+e) if ef ≥ 6 and f ≥ 4. These estimates are deduced from general upper bounds for the number of rational points of bounded height on projective threefolds over Q.
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