$L^p$ maximal estimates for Weyl sums with $k\ge 3$ on $\mathbb{T}$

Xuezhi Chen, Changxing Miao, Jiye Yuan +1

In this paper, we study the $L^p$ maximal estimates for the Weyl sums ${\sum }_{n=1}^N{e}^{2\pi i(nx+n^{k}t)}$ with higher-order $k\ge 3$ on $\mathbb{T}$, and obtain the positive and ne…