17 citations · 64 across the 22 of their papers we have counts for
37 papers
Malle's conjecture and Brauer groups of stacks
Daniel Loughran, Tim Santens
We put forward a conjecture for the leading constant in Malle's conjecture on number fields of bounded discriminant, guided by stacky versions of conjectures of Batyrev-Manin, Baty…
The Hasse norm principle for abelian extensions -- corrigendum
Christopher Frei, Daniel Loughran, Rachel Newton
The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct pr…
Normal distribution of bad reduction
Robert J. Lemke Oliver, Daniel Loughran, Ari Shnidman
We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, of curves in these…
The leading constant for rational points in families
Daniel Loughran, Nick Rome, Efthymios Sofos
We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of variet…
Distribution of genus numbers of abelian number fields
Christopher Frei, Daniel Loughran, Rachel Newton
We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the gen…
The elliptic sieve and Brauer groups
Subham Bhakta, Daniel Loughran, Simon L. Rydin Myerson +1
A theorem of Serre states that almost all plane conics over have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves…