2 citations · 7 across the 8 of their papers we have counts for
9 papers
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…
The leading constant for rational points in families
Daniel Loughran, Nick Rome, Efthymios Sofos
We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of variet…
Weak weak approximation for certain quadric surface bundles
Nick Rome
We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside , some of which appear in the recen…
Average Bateman--Horn for Kummer polynomials
Francesca Balestrieri, Nick Rome
For any and almost all smaller than , we show that the polynomial takes the expected number of prime values as range…
Asymptotics of the -free diffraction measure via discretisation
Nick Rome, Efthymios Sofos
We determine the diffraction intensity of the -free integers near the origin.