On the Waring-Goldbach problem on average

Abstract

Let $s$, $\ell$ be two integers such that $2\le s\le \ell -1$, $\ell \ge 3$. We prove that a suitable asymptotic formula for the average number of representations of integers $n={\sum }_{i=1}^s{p}_i^{\ell }$, where $p_i$, $i=1,\dots ,s$, are prime numbers, holds in short intervals.

arXiv commentPart of this paper will be inserted in arXiv:1810.11357