1 citations · 3 across the 7 of their papers we have counts for
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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, I
R. de la Breteche, T. D. Browning
In this paper the height zeta function associated to a certain singular del Pezzo surface of degree four is studied. If denotes the open subset formed by deleting the unique li…
Counting rational points on hypersurfaces
T. D. Browning, D. R. Heath-Brown
Let be a form of degree , which produces a geometrically irreducible hypersurface in . This paper is concerned with the number of ration…