3 papers
math.NT2026
Lattice coverings and homogeneous covering congruences
J. E. Cremona, P. Koymans
We consider the problem of covering with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this…
math.NT2025
Serre's problem for multiple conics
Stephanie Chan, Peter Koymans, Nick Rome
We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieti…
math.NT2025
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…