Discorrelation between primes in short intervals and polynomial phases

2019/02/13 by Matomäki, Kaisa, Shao, Xuancheng · 1 citation
#11L20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1902.04708

Abstract

Let H = N^θ, θ> 2/3 and k ≥ 1. We obtain estimates for the following exponential sum over primes in short intervals: ∑_{N lt; n ≤ 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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