Discorrelation between primes in short intervals and polynomial phases

Kaisa Matomäki, Xuancheng Shao

Let $H=N^{\theta },\theta >2/3$ and $k\ge 1$. We obtain estimates for the following exponential sum over primes in short intervals: \[ \sum_{N < n \leq N+H} Λ(n) e(g(n)), \] where $g$ is a…