D. R. Heath-Brown

activity

20022022

most citedPair Correlation for Fractional Parts of

α n^{2}

54 citations · 241 across the 42 of their papers we have counts for

collaborators

42 papers

math.NT2022

Equidistribution for Solutions of $p + m^{2} + n^{2} = N$ , and for Châtelet Surfaces

D. R. Heath-Brown

We present a general method for handling problems that ask for the equidistribution of solutions to equations involving $m^{2} + n^{2}$ , and illustrate it by considering $p + m^{2} + n^{2} = N$ .

math.NT2022

The Distribution of Rational Points on Conics

D. R. Heath-Brown

We examine the counting function for rational points on conics, and show how the point where the asymptotic behaviour begins depends on the size of the smallest zero.

math.NT2019★ 2 cited

The Differences Between Consecutive Primes. V

D. R. Heath-Brown

We show that \[\sum_{\substack{p_n\le x\\ p_{n+1}-p_n\ge\sqrt{p_n}}}(p_{n+1}-p_n)\ll_{\varepsilon} x^{3/5+\varepsilon}\] for any fixed $ε > 0$ . This improves a result of Ma…

math.NT2018★ 5 cited

The Differences Between Consecutive Smooth Numbers

D R Heath-Brown

We show that large gaps between smooth numbers are infrequent. The key new tool is a novel mean value bound for a special type of Dirichlet polynomial.

math.NT2018★ 14 cited

Density of rational points on a quadric bundle in $P^{3} \times P^{3}$

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

An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface…

math.NT2017

Iteration of Quadratic Polynomials Over Finite Fields

D. R. Heath-Brown

For a finite field of odd cardinality $q$ , we show that the sequence of iterates of $a X^{2} + c$ , starting at $0$ , always recurs after $O (q / lo g lo g q)$ steps. For $X^{2} + 1$ the same is…

Equidistribution for Solutions of p+m2+n2=N, and for Châtelet Surfaces

The Distribution of Rational Points on Conics

The Differences Between Consecutive Primes. V

The Differences Between Consecutive Smooth Numbers

Density of rational points on a quadric bundle in P3×P3

Iteration of Quadratic Polynomials Over Finite Fields

Equidistribution for Solutions of $p + m^{2} + n^{2} = N$ , and for Châtelet Surfaces

Density of rational points on a quadric bundle in $P^{3} \times P^{3}$