6 citations · 40 across the 25 of their papers we have counts for
8 papers · 1 filter
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…
On a Hybrid Version of the Vinogradov Mean Value Theorem
Changhao Chen, Igor E. Shparlinski
Given a family of distinct nonconstant polynomials, a positive integer and a real positive parameter , we consider the me…
On uniform distribution of -orbits
Changhao Chen, Xiaohua Wang, Shengyou Wen
Let such that at least one of them is irrational. We take a random walk on the real line such that the choice of and has equal probability . We prove t…
Small values of Weyl sums
Changhao Chen, Igor E. Shparlinski
We prove that the set of , such that contains a…
Hausdorff dimension of the large values of Weyl sums
Changhao Chen, Igor E. Shparlinski
The authors have recently obtained a lower bound of the Hausdorff dimension of the sets of vectors with large Weyl sums, namely of vectors for which…
New bounds of Weyl sums
Changhao Chen, Igor E. Shparlinski
We augment the method of Wooley (2015) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real poly…
Discretized sum-product for large sets
Changhao Chen
Let be a -set with measure in the sense of Katz and Tao. For we show that for $c=\frac…
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…