24 citations · 171 across the 47 of their papers we have counts for
6 papers · 2 filters
An overview of Manin's conjecture for del Pezzo surfaces
T. D. Browning
This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound o…
Simultaneous equal sums of three powers
T. D. Browning, D. R. Heath-Brown
Using a recent result of Salberger, we establish the paucity of non-trivial positive integer solutions to a certain system of diagonal Diophantine equations.
Equal sums of like polynomials
T. D. Browning
Let be a polynomial of degree , with integer coefficients. Then the paucity of non-trivial positive integer solutions to the equation is established.…
Plane curves in boxes and equal sums of two powers
T. D. Browning, D. R. Heath-Brown
Given an absolutely irreducible ternary form , the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are rest…
The density of rational points on non-singular hypersurfaces, II
T. D. Browning, D. R. Heath-Brown
This paper establishes the conjecture that a non-singular projective hypersurface of dimension , which is not equal to a linear space, contains rational points of h…
On Manin's conjecture for singular del Pezzo surfaces of degree four, II
R. de la Breteche, T. D. Browning
This paper establishes the Manin conjecture for a certain non-split singular del Pezzo surface of degree four, via an analysis of the corresponding height zeta function.