Let $H = N^{\theta }, \theta> 2/3$ and $k \geq 1$. We obtain estimates for the following exponential sum over primes in short intervals: \begin{equation*} \sum_{N < n \leq N+H} \Lambda(n) \mathrm e(g(n)), \end{equation*}where $g$ is a polynomial of degree $k$. As a consequence of this in the special case $g(n) = \alpha n^k$, we deduce a short interval version of the Waring–Goldbach problem.
more » « less Award ID(s):
 1802224
 NSFPAR ID:
 10116959
 Publisher / Repository:
 Oxford University Press
 Date Published:
 Journal Name:
 International Mathematics Research Notices
 ISSN:
 10737928
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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