5 papers
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…