D. R. Heath-Brown

activity

20062025

most citedDensity of non-residues in Burgess-type intervals and applications

19 citations · 25 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2025

Manin's conjecture for quintic del Pezzo surfaces with a conic bundle structure

D. R. Heath-Brown, Daniel Loughran

We investigate Manin's conjecture for del Pezzo surfaces of degree five with a conic bundle structure, proving matching upper and lower bounds, and the full conjecture in the Galoi…

math.NT2025

$ℓ$ -Torsion in Class Groups via Dirichlet $L$ -functions

D. R. Heath-Brown

For a prime $ℓ$ , let $h_{ℓ} (K)$ denote the $ℓ$ -part of the class number of the number field $K$ . We investigate upper bounds for $h_{ℓ} (K)$ when $K$ is quadratic or cubic,…

math.NT2023

Bounds for the Quartic Weyl Sum

D. R. Heath-Brown

We improve the standard Weyl estimate for quartic exponential sums in which the argument is a quadratic irrational. Specifically we show that \[\sum_{n\le N} e(αn^4)\ll_{\ep,α}N^{5…

math.NT2010★ 6 cited

A Note on the Chevalley--Warning Theorems

D. R. Heath-Brown

Let $f_{1}, . ˙ ., f_{r}$ be polynomials in $n$ variables over a finite field $F$ of cardinality $q$ and characteristic $p$ . Let $f_{i}$ have total degree $d_{i}$ and define $d = d_{1} + . ˙ . + d_{r}$ .…

math.NT2006★ 19 cited

Density of non-residues in Burgess-type intervals and applications

W. D. Banks, M. Z. Garaev, D. R. Heath-Brown +1

We show that for any fixed $\eps>0$, there are numbers $δ > 0$ and $p_{0} \geq 2$ with the following property: for every prime $p \geq p_{0}$ and every integer $N$ such that $p^{1/(4\sqrt{e}…

Manin's conjecture for quintic del Pezzo surfaces with a conic bundle structure

ℓ-Torsion in Class Groups via Dirichlet L-functions

Bounds for the Quartic Weyl Sum

A Note on the Chevalley--Warning Theorems

Density of non-residues in Burgess-type intervals and applications

$ℓ$ -Torsion in Class Groups via Dirichlet $L$ -functions