Vinogradov's theorem with almost equal summands

Kaisa Matomäki, James Maynard, Xuancheng Shao

Let $\theta >11/20$. We prove that every sufficiently large odd integer $n$ can be written as a sum of three primes $n=p_1+p_2+p_3$ with $|p_i-n/3|\le n^{\theta }$ for $i\in \{1,2,3\}$…