Sums of primes and squares of primes in short intervals

Details Sums of primes and squares of primes in short intervals Sums of primes and squares of primes in short intervals

2007-12-30

arxiv.org/abs/0801.0130v1

Monatsh. Math. 157 (2009), 335-363

Mathematics

Number Theory

Scientific paper

Let $\mathbf H_2$ denote the set of even integers $n \not\equiv 1 \pmod 3$.
We prove that when $H \ge X^{0.33}$, almost all integers $n \in \mathbf H_2$,
$X < n \le X + H$ can be represented as the sum of a prime and the square of a
prime. We also prove a similar result for sums of three squares of primes.

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