Bounds on the Norms of Maximal Operators on Weyl Sums

Roger C. Baker; Changhao Chen; Igor E. Shparlinski

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arXiv · 2107.13674

Bounds on the Norms of Maximal Operators on Weyl Sums

Roger C. Baker·Changhao Chen·Igor E. Shparlinski

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Abstract

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).

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Roger C. Baker, Changhao Chen, Igor E. Shparlinski. 2021-07-29. Bounds on the Norms of Maximal Operators on Weyl Sums. https://arxiv.org/abs/2107.13674

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