Yukai Wang

Many Representations as Sums of Three Prime Cubes

Let $F_k(n)$ be the number of unordered representations \[ n=p_1^k+p_2^k+\cdots +p_k^k \] by primes, with repetitions allowed. Erd\H{o}s stated that $\limsup_{n\to\infty} F_3(n)=\infty$, but his proof appears not to have been published. A complete unconditional proof is given. The principal input is the classical Hecke...