Philippa Holdridge

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20232026

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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.NT2023

Random Diophantine Equations in the Primes II

Philippa Holdridge

Let $d \geq 2$ and $n \geq d$ with $(d, n) \in / {(2, 2), (3, 3)}$ . We consider homogeneous Diophantine equations of degree $d$ in $n + 1$ variables and whether they have solutions in the…