3 papers
math.NT2026
The leading constant in Malle's conjecture
Daniel Loughran, Tim Santens
We give an overview of a recent conjecture of the authors on the leading constant in Malle's conjecture on number fields of bounded discriminant. This comes from applying the philo…
math.NT2025
Campana points on wonderful compactifications
Dylon Chow, Daniel Loughran, Ramin Takloo-Bighash +1
We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a ne…
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…