Counting Rational Points on Algebraic Varieties

By Tim D Browning, D. R. Heath-Brown, P. Salberger. 2004

114 citations recorded by the source corpus.

For any N � 2, let ZP N be a geometrically integral algebraic variety of degree d. This paper is concerned with the number NZ(B) of Q-rational points on Z which have height at most B. For any " > 0 we establish the estimate

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7b65f58901921070a710d9bbd89cbf33af270a85

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Tim D Browning

In Computational Theory and Mathematics

1. Tim D Browning

In Geometry and Topology

1. R. Dietmann
2. Tim D Browning
3. Manjul Bhargava
4. Ulrich Derenthal

Citations in the corpus

• ON THE DISTRIBUTION OF GALOIS GROUPS (2010, background): “After homogenizing F , this becomes the special case P1 = 1 of Theorem 1 in [2]; see also formula (3) there, and see [11], Theorem 15 for an earlier reference for this result.”
• Power-free values of polynomials (2011, methodology): “More recently, Heath-Brown [6] has shown that one may take k > 3d 4 + 1 2 .”