23 citations · 25 across the 10 of their papers we have counts for
12 papers
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…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
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…
The Brauer-Manin obstruction for stacky curves
Tim Santens
We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This incl…
Diagonal quartic surfaces with a Brauer-Manin obstruction
Tim Santens
In this paper we investigate the quantity of diagonal quartic surfaces which have a Brauer-Manin obstruction to the Hasse princip…
Integral points on affine quadric surfaces
Tim Santens
It is well-known that the Hasse principle holds for quadric hypersurfaces. The Hasse principle fails for integral points on smooth quadric hypersurfaces of dimension 2 but the fail…