4 citations · 8 across the 8 of their papers we have counts for
8 papers
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; this may be viewed as a projective, or homogeneous, version of the well-know…
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…
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…
Elliptic curves and spin
Peter Koymans, Peter Vang Uttenthal
In the early 2000s, Ramakrishna asked the question: For the elliptic curve what is the density of primes for which the Fourier coefficient is a…
A note on the Hasse norm principle
Peter Koymans, Nick Rome
Let be a finite, abelian group. We show that the density of -extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This str…
Weak approximation on the norm one torus
Peter Koymans, Nick Rome
For any abelian group , we prove an asymptotic formula for the number of -extensions of bounded discriminant such that the associated norm one torus $R_{K/\mat…
Vinogradov's three primes theorem with primes having given primitive roots
Christopher Frei, Peter Koymans, Efthymios Sofos
The first purpose of our paper is to show how Hooley's celebrated method leading to his conditional proof of the Artin conjecture on primitive roots can be combined with the Hardy-…
The Catalan Equation in Finitely Generated Domains
Peter Koymans
We consider the Catalan equation in unknowns , where are taken from an integral domain of characteristic that is finitely generated as a…