Sum of one prime and two squares of primes in short intervals

Alessandro Languasco, Alessandro Zaccagnini

Published 2014-06-13, updated 2014-08-24Version 2

For sufficiently large $N$ we prove that the interval $[N,N+H]$, $H\ge N^{7/12+\epsilon}$, contains an integer which is a sum of a prime and two squares of primes. If we assume the Riemann Hypothesis we can take $H \ge C (\log N)^{4}$, where $C >0$ is an effective constant.