6 citations · 6 across the 3 of their papers we have counts for
4 papers
The geometric sieve for quadrics
Tim Browning, Roger Heath-Brown
We develop a version of Ekedahl's geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to comp…
Counting rational points on quadric surfaces
T. D. Browning, D. R. Heath-Brown
We give an upper bound for the number of rational points of height at most , lying on a surface defined by a quadratic form . The bound shows an explicit dependence on . I…
Almost prime triples and Chen's Theorem
D. R. Heath-Brown, Xiannan Li
We show that there are infinitely many primes such that not only does have at most two prime factors, but also has a bounded number of prime divisors. This refi…
Counting Rational Points on Cubic Curves
D. R. Heath-Brown, D. Testa
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the cor…