2023/10/03 by Holdridge, Philip
#11D45 #11P21 #11P32 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2310.02137
Let d≥ 2 and n≥ d with (d,n)∉ \(2,2),(3,3)\. We consider homogeneous Diophantine equations of degree d in n+1 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 the author arXiv:2305.06306. We do this by adapting the methods of Browning, Le Boudec and Sawin (Annals, 2023).