Roger C. Baker, Changhao Chen, Igor E. Shparlinski
Published 2021-07-29Version 1
We obtain new estimates on the maximal operator applied to the Weyl sums. We also consider the quadratic case (that is, Gauss sums) in more details. In wide ranges of parameters our estimates are optimal and match lower bounds. Our approach is based on a combination of ideas of Baker (2021) and Chen and Shparlinski (2020).
Perturbations of Weyl sums
$L^p$ maximal estimates for Weyl sums with $k\ge3$ on $\mathbb{T}$
Metric theory of Weyl sums
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