Chang-Pao Chen

activity

20132023

most citedLocally rich compact sets

6 citations · 40 across the 25 of their papers we have counts for

collaborators

29 papers

math.NT2023

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…

math.NT2021

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 $α \in (1/2, 1)$ achieve the order at least $N^{α}$ for infinitely many…

math.NT2021

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…

math.CA2020★ 3 cited

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…

math.NT2020

Metric theory of lower bounds on Weyl sums

Changhao Chen, Bryce Kerr, Igor Shparlinski

We prove that the Hausdorff dimension of the set $x \in [0, 1)^{d}$ , 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}…

math.CA2020★ 5 cited

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 $k \geq 2$ polynomials of the form $(τ x + c) ω (n) + x n$ , $n = 1, 2, \dots$ , with fixed $ω (T) \in Z [T]$ and $τ \in R$ , which…

math.CA2019★ 3 cited

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 $X \subseteq [0, 1)^{d}$ with a natural measure $μ$ on $X$ . For certain measure spa…

math.CA2019★ 1 cited

On a Hybrid Version of the Vinogradov Mean Value Theorem

Changhao Chen, Igor E. Shparlinski

Given a family $φ = (φ_{1}, \dots, φ_{d}) \in Z [T]^{d}$ of $d$ distinct nonconstant polynomials, a positive integer $k \leq d$ and a real positive parameter $ρ$ , we consider the me…

math.CA2019

On uniform distribution of $α β$ -orbits

Changhao Chen, Xiaohua Wang, Shengyou Wen

Let $α, β \in (0, 1)$ such that at least one of them is irrational. We take a random walk on the real line such that the choice of $α$ and $β$ has equal probability $1/2$ . We prove t…

math.NT2019

Small values of Weyl sums

Changhao Chen, Igor E. Shparlinski

We prove that the set of $(x_{1}, \dots, x_{d}) \in [0, 1)^{d}$ , such that $lim_{N \to \infty} n = 1 \sum N exp (2 π i (x_{1} n + \dots + x_{d} n^{d})) = 0,$ contains a…

math.CA2019

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 $(x_{1}, \dots, x_{d}) \in [0, 1)^{d}$ with large Weyl sums, namely of vectors for which…

math.CA2019

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…

math.CO2019★ 2 cited

Discretized sum-product for large sets

Changhao Chen

Let $A \subset [1, 2]$ be a $(δ, σ)$ -set with measure $∣ A ∣ = δ^{1 - σ}$ in the sense of Katz and Tao. For $σ \in (1/2, 1)$ we show that $∣ A + A ∣ + ∣ AA ∣ ⪆ δ^{- c} ∣ A ∣,$ for $c=\frac…

math.NT2019

On Large Values of Weyl Sums

Changhao Chen, Igor E. Shparlinski

A special case of the Menshov--Rademacher theorem implies for almost all polynomials $x_{1} Z + \dots + x_{d} Z^{d} \in R [Z]$ of degree $d$ for the Weyl sums satisfy the upper b…

math.CO2018★ 2 cited

A new sum-product estimate in prime fields

Changhao Chen, Bryce Kerr, Ali Mohammadi

In this paper we obtain a new sum-product estimate in prime fields. In particular, we show that if $A \subseteq F_{p}$ satisfies $∣ A ∣ \leq p^{64/117}$ then $$ \max\{|A\pm A|, |…

math.CO2018

Threshold functions for substructures in random subsets of finite vector spaces

Changhao Chen, Catherine Greenhill

The study of substructures in random objects has a long history, beginning with Erdős and Rényi's work on subgraphs of random graphs. We study the existence of certain substructure…

math.CA2017★ 1 cited

Finite field analogue of restriction theorem for general measures

Changhao Chen

We study restriction problem in vector spaces over finite fields. We obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem, and we show that the range…

math.CA2017★ 1 cited

Restricted families of projections in vector spaces over finite fields

Changhao Chen

We study the restricted families of projections in vector spaces over finite fields. We show that there are families of random subspaces which admit a Marstrand-Mattila type projec…

math.CA2017★ 5 cited

Restricted families of projections and random subspaces

Changhao Chen

We study the restricted families of orthogonal projections in $R^{3}$ . We show that there are families of random subspaces which admit a Marstrand- Mattila type projection t…

math.CA2017

Salem sets in vector spaces over finite fields

Changhao Chen

We prove that almost all random subsets of a finite vector space are weak Salem sets (small Fourier coefficient), which extends a result of Hayes to a different probability model.

math.CA2017★ 1 cited

Projections in vector spaces over finite fields

Changhao Chen

We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapp…

math.MG2016★ 4 cited

Accessible values of Assouad and the lower dimensions of subsets

Changhao Chen, Meng Wu, Wen Wu

Let $E$ be a subset of a doubling metric space $(X, d)$ . We prove that for any $s \in [0, dim_{A} E]$ , where $dim_{A}$ denotes the Assouad dimension, there exists a subset $F$ of $E…

math.PR2016

A class of random Cantor sets

Changhao Chen

In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also comp…

math.CA2015★ 1 cited

Intersection properties of typical compact sets

Changhao Chen

We prove that a typical compact set does not contain any similar copy of a given pattern. We also prove that a typical compact set of $[0, 1]^{d} (d \geq 2)$ intersects any $(d - 1)$ -d…

Local mean value estimates for Weyl sums

Large Weyl sums and Hausdorff dimension

Bounds on the Norms of Maximal Operators on Weyl Sums

Self-similar sets with super-exponential close cylinders

Metric theory of lower bounds on Weyl sums

Hybrid bounds on two-parametric family Weyl sums along smooth curves

Restricted mean value theorems and metric theory of restricted Weyl sums

On a Hybrid Version of the Vinogradov Mean Value Theorem

On uniform distribution of αβ-orbits

Small values of Weyl sums

Hausdorff dimension of the large values of Weyl sums

New bounds of Weyl sums

Discretized sum-product for large sets

On Large Values of Weyl Sums

A new sum-product estimate in prime fields

Threshold functions for substructures in random subsets of finite vector spaces

Finite field analogue of restriction theorem for general measures

Restricted families of projections in vector spaces over finite fields

Restricted families of projections and random subspaces

Salem sets in vector spaces over finite fields

Projections in vector spaces over finite fields

Accessible values of Assouad and the lower dimensions of subsets

A class of random Cantor sets

Intersection properties of typical compact sets

On uniform distribution of $α β$ -orbits