17 citations · 27 across the 10 of their papers we have counts for
11 papers
Odd order cases of Chowla's averages over arbitrary rectangles
Qiang Huo, Zhengxing Lian, Kangbo Ouyang
Let be the Liouville function. In this paper we prove an average form of Chowla Conjecture for even . that is, for every fixed even integer , we prove that \[ \lim…
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
Maximal pronilfactors and a topological Wiener-Wintner theorem
Yonatan Gutman, Zhengxing Lian
For strictly ergodic systems, we introduce the class of CF-Nil() systems: systems for which the maximal measurable and maximal topological -step pronilfactors coincide as mea…
Pro-nilfactors of the space of arithmetic progressions in topological dynamical systems
Zhengxing Lian, Jiahao Qiu
For a topological dynamical system , and , let and be the orbit closures of the diagonal point ( times) un…
Minimal systems with finitely many ergodic measures
Wen Huang, Zhengxing Lian, Song Shao +1
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measur…
A counter-example for polynomial version of Sarnak's conjecture
Zhengxing Lian, Ruxi Shi
We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the Möbius function is linearly disjoint from subsequences alo…
Strictly ergodic distal models and a new approach to the Host-Kra factors
Yonatan Gutman, Zhengxing Lian
Cocycles are a key object in Antolín Camarena and Szegedy's (topological) theory of nilspaces. We introduce measurable counterparts, named nilcycles, enabling us to give conditions…
Reducing the Sarnak Conjecture to Toeplitz systems
Wen Huang, Zhengxing Lian, Song Shao +1
In this paper, we show that for any sequence and any , there exists a Toeplitz sequence ${\bf b}=(b_n)_{n\in \Z}\in \{1,…
Affine transformation with zero entropy and nilsystems
Zhengxing Lian
In this paper, we study affine transformations on tori, nilmanifolds and compact abelian groups. For these systems, we show that an equivalent condition for zero entropy is the orb…
Sequences from zero entropy noncommutative toral automorphisms and Sarnak Conjecture
Wen Huang, Zhengxing Lian, Song Shao +1
In this paper we study -algebra version of Sarnak Conjecture for noncommutative toral automorphisms. Let be a noncommutative torus and be the noncommutative toral…
Weakly mixing, proximal topological models for ergodic systems and applications
Zhengxing Lian, Song Shao, Xiangdong Ye
In this paper it is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal poin…