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

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.

removed unconditional case; other minor changes inserted

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• A remark on the conditional estimate for the sum of a prime and a square
• On the average number of representations of an integer as a sum of polynomials computed at prime values
• On an average ternary problem with prime powers