Sums of almost equal squares of primes

Angel Kumchev, Taiyu Li

We study the representations of large integers $n$ as sums $p_1^2+...+p_s^2$, where $p_1,...,p_s$ are primes with $|p_i-(n/s{)}^{1/2}|\le n^{\theta /2}$, for some fixed $\theta <1$. W…