Sam Chow

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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.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 $b$ …