Maximal estimates for the Weyl sums on ${\mathbb{T}}^d$ (with an appendix by Alex Barron)

Changxing Miao, Jiye Yuan, Tengfei Zhao

In this paper, we obtain the maximal estimate for the Weyl sums on the torus ${\mathbb{T}}^d$ with $d\ge 2$, which is sharp up to the endpoint. We also consider two variants of this…