5 citations · 19 across the 11 of their papers we have counts for
20 papers
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…
Self-similar sets with super-exponential close cylinders
Changhao Chen
S. Baker (2019), B. Bárány and A. Käenmäki (2019) independently showed that there exist iterated function systems without exact overlaps and there are super-exponentially close cyl…
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}…
Hybrid bounds on two-parametric family Weyl sums along smooth curves
Changhao Chen, Igor E. Shparlinski
We obtain a new bound on Weyl sums with degree polynomials of the form , , with fixed and , which…
Restricted mean value theorems and metric theory of restricted Weyl sums
Changhao Chen, Igor E. Shparlinski
We study an apparently new question about the behaviour of Weyl sums on a subset with a natural measure on . For certain measure spa…