Philippa Holdridge

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20232026

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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…

math.NT2023

Random Diophantine Equations in the Primes

Philippa Holdridge

We consider equations of the form $a_{1} x_{1}^{k} + ... + a_{s} x_{s}^{k}$ and when they have solutions in the primes. We define an analogue of the Hasse principle for solubility in the…