Sam Chow

collaborators

4 papers

math.NT2024

Additive Ramsey theory over Piatetski-Shapiro numbers

Jonathan Chapman, Sam Chow, Philippa Holdridge

We characterise partition regularity for linear equations over the Piatetski-Shapiro numbers $⌊ n^{c} ⌋$ when $1 < c < c^{†} (s)$ , where $s ⩾ 3$ is the number of var…

math.CO2024

Incidence geometry and polynomial expansion over finite fields

Nuno Arala, Sam Chow

We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemerédi--Trotter-type theorem over finite fields, with an application to polynomial expan…

math.CO2024

Expansion properties of polynomials over finite fields

Nuno Arala, Sam Chow

We establish expansion properties for suitably generic polynomials of degree $d$ in $d + 1$ variables over finite fields. In particular, we show that if $P\in\mathbb{F}_q[x_1,\ldots,…

math.NT2024

Arithmetic Ramsey theory over the primes

Jonathan Chapman, Sam Chow

We study density and partition properties of polynomial equations in prime variables. We consider equations of the form $a_{1} h (x_{1}) + \dots + a_{s} h (x_{s}) = b$ , where the $a_{i}$ and $b$ …