A density version for the sum of nine cubes of primes

Kaijie Li, Tianze Wang, Xiaodong Zhao

Let $\mathbb{P}$ be the set of primes. Suppose that $P_i$, $i=1,2,\dots ,9$ are nine subsets of $\mathbb{P}$ with relative lower density ${\underline{d}}_{\mathbb{P}}(P_i)={\mu }_i$…