Cameron Wilson

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math.NT2025

An improved large sieve for quadratic characters via Hooley neutralisers and its applications

Cameron Wilson

We combine Hooley neutralisers and the large sieve for quadratic characters. We give applications to character sums with a hyperbolic height condition.

math.NT2025

Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface

Cameron Wilson

We prove asymptotics for the density of everywhere locally soluble diagonal quadric surfaces parameterised by rational points on the split quadric surface $y_{0} y_{1} = y_{2} y_{3}$ which do…

math.NT2024

Local solubility of a family of ternary conics over a biprojective base I

Cameron Wilson

Let $f, g \in Z [u_{1}, u_{2}]$ be binary quadratic forms. We provide upper bounds for the number of rational points $(u,v)\in\mathbb{P}^1(\mathbb{Q})\times\mathbb{P}^1(\mathbb{Q})…

math.NT2024

Higher Moments for Polynomial Chowla

Cameron Wilson

Let $I^» (n)$ be the Liouville function. We study the distribution of \[ \frac{1}{x^{1/2}}\sum_{x\leq n\leq 2x}Î»(f(n)) \] over random polynomials $f$ of fixed degree $d$ and coeffic…