Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which is a sum of a prime and two squares of primes provided that $H \ge C (\log N)^{4}$, where $C >0$ is an effective constant.
Sum of one prime and two squares of primes in short intervals
LANGUASCO, ALESSANDRO;
2016
Abstract
Assuming the Riemann Hypothesis we prove that the interval $[N,N+H]$ contains an integer which is a sum of a prime and two squares of primes provided that $H \ge C (\log N)^{4}$, where $C >0$ is an effective constant.
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