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, Batyrev …

Let GG be a nontrivial finite étale tame group scheme over a global field F F. We define
height functions on the set of GG‐torsors over FF, which generalize the usual heights such …

We consider the problem of counting the number of varieties in a family over Q with a
rational point. We obtain lower bounds for this counting problem for some families over P1 …

Weak approximation on the norm one torus Page 1 Weak approximation on the norm one
torus P. Koymans and N. Rome Compositio Math. 160 (2024), 1304–1348. doi:10.1112/S0010437X24007103 …

We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in
which algebraic tori are replaced with finite supersolvable groups. As an application, we …

Given a number field $ k $ and a finitely generated subgroup $\mathcal {A}\subseteq k^* $,
we study the distribution of $ S_4 $-quartic extensions of $ k $ such that the elements of …

Let AA be a finite, abelian group. We show that the density of AA‐extensions satisfying the
Hasse norm principle exists, when the extensions are ordered by discriminant. This …

The inverse Galois problem asks whether any finite group can be realised as the Galois
group of a Galois extension of the rationals. This problem and its refinements have …

Let K/k be an extension of number fields. We describe theoretical results and computational
methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of …

Distribution of genus numbers of abelian number fields - Frei - 2023 - Journal of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article Information …