Corpus ID: 236493773

Bounds on the Norms of Maximal Operators on Weyl Sums

@inproceedings{Baker2021BoundsOT,
  title={Bounds on the Norms of Maximal Operators on Weyl Sums},
  author={Roger C. Baker and Changhao Chen and Igor E. Shparlinski},
  year={2021}
}
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). 
Large Weyl sums and Hausdorff dimension
Abstract. We obtain the exact value of the Hausdorff dimension of the set of coefficients of Gauss sums which for a given α ∈ (1/2, 1) achieve the order at least Nα for infinitely many sum lengths NExpand

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