5 citations · 19 across the 11 of their papers we have counts for
6 papers · 1 filter
Local mean value estimates for Weyl sums
Julia Brandes, Changhao Chen, Igor E. Shparlinski
We obtain new estimates - both upper and lower bounds - on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures o…
Large Weyl sums and Hausdorff dimension
Roger C. Baker, Changhao Chen, Igor E. Shparlinski
We obtain the exact value of the Hausdorff dimension of the set of coefficients of Gauss sums which for a given achieve the order at least for infinitely many…
Bounds on the Norms of Maximal Operators on Weyl Sums
Roger C. Baker, Changhao Chen, Igor E. Shparlinski
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 ou…
Metric theory of lower bounds on Weyl sums
Changhao Chen, Bryce Kerr, Igor Shparlinski
We prove that the Hausdorff dimension of the set , such that $$ \left|\sum_{n=1}^N \exp\left(2 πi\left(x_1n+\ldots+x_d n^d\right)\right) \right|\ge c N^{1/2}…
Small values of Weyl sums
Changhao Chen, Igor E. Shparlinski
We prove that the set of , such that contains a…
On Large Values of Weyl Sums
Changhao Chen, Igor E. Shparlinski
A special case of the Menshov--Rademacher theorem implies for almost all polynomials of degree for the Weyl sums satisfy the upper b…