23 citations · 25 across the 10 of their papers we have counts for
8 papers · 1 filter
A refined Malle conjecture for Heisenberg groups
Jack B. Miller, Tim Santens
Based on a conjecture of Loughran and the second author, we give an explicit prediction for the leading constant in Malle's conjecture for Galois -extensions of $\math…
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…
The leading constant in Malle's conjecture over function fields
Tim Santens
We prove the analogue of Malle's conjecture for the global function field $\F_q(t)$ with sufficiently large, including a precise formula for the leading constant. The main ingr…
Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Per Salberger +2
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least . For degrees and we improve the known boun…
Counting points on some genus zero Shimura curves
Tyler Genao, Tristan Phillips, Fredderick Saia +2
We count certain abelian surfaces with potential quaternionic multiplication defined over a number field by counting points of bounded height on some genus zero Shimura curves.
Local solubility of generalised Fermat equations
Peter Koymans, Ross Paterson, Tim Santens +1
For every we determine the asymptotic formula for the number of integer triples of bounded absolute value such that the generalised Fermat equation given by $a…
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…
Manin's conjecture for integral points on toric varieties
Tim Santens
We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded he…