Bounds on the norms of maximal operators on Weyl sums

Roger C Baker,Changhao Chen,Igor E Shparlinski

doi:10.1016/j.jnt.2023.10.001

Bounds on the norms of maximal operators on Weyl sums

Roger C Baker, Changhao Chen + Show 1 more

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https://doi.org/10.1016/j.jnt.2023.10.001

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Journal: Journal of number theory

Publication Date: Nov 4, 2023

Affiliation: Brigham Young University, Anhui University, UNSW Sydney

#Gauss Sums #Quadratic Case + Show 3 more

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Abstract

We obtain new estimates on the maximal operator applied to the Weyl sums, which are tight in some cases. 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).

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