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

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Showing 2008Show all

2 papers · 1 filter

math.NT2008★ 1 cited

Zeros of Systems of $p$ -adic Quadratic Forms

D. R. Heath-Brown

It is shown that a system of $r$ quadratic forms over a $p$ -adic field has a non-trivial common zero as soon as the number of variables exceeds $4 r$ , providing that the…

math.NT2008

Sums and Differences of Three k-th Powers

D. R. Heath-Brown

Let k>2 be a fixed integer exponent and let θ> 9/10. We show that a positive integer N can be represented as a non-trivial sum or difference of 3 k-th powers, using integers of siz…

Zeros of Systems of p-adic Quadratic Forms

Sums and Differences of Three k-th Powers

Zeros of Systems of $p$ -adic Quadratic Forms