Nick Rome

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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.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

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

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