D. R. Heath-Brown

collaborators

3 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…

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

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