Random Diophantine equations in the primes II
Abstract
Abstract Let and with . We consider homogeneous Diophantine equations of degree in variables and whether they have solutions in the primes. In particular, we show that a certain local–global principle holds for almost all such equations, following on from previous work of Holdridge. We do this by adapting the methods of Browning, Le Boudec and Sawin, with the main input coming from some results on counting points with prime coordinates in lattices.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN