10 citations · 13 across the 3 of their papers we have counts for
4 papers
Forms in many variables and differing degrees
T. D. Browning, D. R. Heath-Brown
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle…
Simultaneous Integer Values of Pairs of Quadratic Forms
D. R. Heath-Brown, L. B. Pierce
We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, pr…
Burgess's Bounds for Character Sums
Roger Heath-Brown
We prove that Burgess's bound gives an estimate not just for a single character sum, but for a mean value of many such sums.
Zeros of p-adic forms
D. R. Heath-Brown
A variant of Brauer's induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably…