D. R. Heath-Brown

activity

20022009

most citedThe density of rational points on Cayley's cubic surface

33 citations · 42 across the 11 of their papers we have counts for

collaborators

Showing 2005Show all

4 papers · 1 filter

math.NT2005★ 1 cited

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.

math.NT2005

Plane curves in boxes and equal sums of two powers

T. D. Browning, D. R. Heath-Brown

Given an absolutely irreducible ternary form $F$ , 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…

math.NT2005

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 $r$ , which is not equal to a linear space, contains $O (B^{r + ε})$ rational points of h…

math.NT2005

The density of rational points on non-singular hypersurfaces, I

T. D. Browning, D. R. Heath-Brown

Let $X \subset P^{n}$ be a non-singular hypersurface of degree $d > 1$ , and let $ε > 0$ . This paper is concerned with the conjecture that there are $O (B^{n - 1 + ε})$ rational point…