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arXiv · 1902.04708

Discorrelation between primes in short intervals and polynomial phases

Kaisa Matomäki·Xuancheng Shao
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Abstract

Let $H = N^θ, θ> 2/3$ and $k \geq 1$. 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 polynomial of degree $k$. As a consequence of this in the special case $g(n) = αn^k$, we deduce a short interval version of the Waring-Goldbach problem.

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Kaisa Matomäki, Xuancheng Shao. 2019-06-26. Discorrelation between primes in short intervals and polynomial phases. https://arxiv.org/abs/1902.04708

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