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arXiv · 2203.12168

Averages of exponential twists of the von Mangoldt function

Xiumin Ren·Wei Zhang
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Abstract

In this paper, we obtain some improved results for the exponential sum $\sum_{x<n\leq 2x}\Lambda(n)e(\alpha k n^{\theta})$ with $\theta\in(0,5/12),$ where $\Lambda(n)$ is the von Mangoldt function. Such exponential sums have relations with the so-called quasi-Riemann hypothesis and were considered by Vinogradov \cite{Va} and Murty-Srinivas \cite{Mu}.

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Xiumin Ren, Wei Zhang. 2022-03-23. Averages of exponential twists of the von Mangoldt function. https://doi.org/10.1017/s0004972722000430

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