Nick Rome

collaborators

3 papers

math.NT2019

Asymptotics of the $k$ -free diffraction measure via discretisation

Nick Rome, Efthymios Sofos

We determine the diffraction intensity of the $k$ -free integers near the origin.

math.AG2019

Fields of definition of curves of a given degree

David Holmes, Nick Rome

Kontsevich and Manin gave a formula for the number $N_{e}$ of rational plane curves of degree $e$ through $3 e - 1$ points in general position in the plane. When these $3 e - 1$ points hav…

math.NT2018

A Positive Proportion of Hasse Principle Failures in a Family of Châtelet Surfaces

Nick Rome

We investigate the family of surfaces defined by the affine equation $Y^{2} + Z^{2} = (a T^{2} + b) (c T^{2} + d)$ where $∣ a d - b c ∣ = 1$ and develop an asymptotic formula for the frequ…

Asymptotics of the k-free diffraction measure via discretisation

Fields of definition of curves of a given degree

A Positive Proportion of Hasse Principle Failures in a Family of Châtelet Surfaces

Asymptotics of the $k$ -free diffraction measure via discretisation