Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic ...Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic cocycles which are almost reducible,which extends(Liu and Sarnak in Duke Math J 164(7):1353–1399,2015;Wang in Invent Math 209:175–196,2017)to the noncommutative case.The proof relies on quantitative version of almost reducibility.展开更多
The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential ...The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.展开更多
The main purpose of this paper is to define prime and introduce non-commutative arithmetics based on Thompson's group F.Defining primes in a non-abelian monoid is highly non-trivial,which relies on a concept calle...The main purpose of this paper is to define prime and introduce non-commutative arithmetics based on Thompson's group F.Defining primes in a non-abelian monoid is highly non-trivial,which relies on a concept called"castling".Three types of castlings are essential to grasp the arithmetics.The divisor functionτon Thompson's monoid S satisfiesτ(uv)≤τ(u)τ(v)for any u,v∈S.Then the limitτ_(0)(u)=lim_(n→∞)(τ(u~n))^(1/n)exists.The quantityC(S)=sup_(1≠u∈S)τ_(0)(u)/τ(u)describes the complexity for castlings in S.We show thatC(S)=1.Moreover,the MCbius function on S is calculated.And the Liouville functionCon S is studied.展开更多
基金Tianyuan Mathematical Center in Southwest(No.11826102)supported by NSFC grant(Nos.12090012,12031019,12090010)+8 种基金supported by National Key R&D Program of China(No.2021YFA1001600)NSFC grant(No.11971233)the Outstanding Youth Foundation of Jiangsu Province(No.BK20200074)Qing Lan Project of Jiangsu provincesupported by NSF grant(No.DMS-1753042)supported by National Key R&D Program of China(No.2020YFA0713300)NSFC grant(No.12071232)The Science Fund for Distinguished Young Scholars of Tianjin(No.19JCJQJC61300)Nankai Zhide Foundation.
文摘Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic cocycles which are almost reducible,which extends(Liu and Sarnak in Duke Math J 164(7):1353–1399,2015;Wang in Invent Math 209:175–196,2017)to the noncommutative case.The proof relies on quantitative version of almost reducibility.
文摘The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.
基金Supported by National Natural Science Foundation of China(Grant No.11701549)。
文摘The main purpose of this paper is to define prime and introduce non-commutative arithmetics based on Thompson's group F.Defining primes in a non-abelian monoid is highly non-trivial,which relies on a concept called"castling".Three types of castlings are essential to grasp the arithmetics.The divisor functionτon Thompson's monoid S satisfiesτ(uv)≤τ(u)τ(v)for any u,v∈S.Then the limitτ_(0)(u)=lim_(n→∞)(τ(u~n))^(1/n)exists.The quantityC(S)=sup_(1≠u∈S)τ_(0)(u)/τ(u)describes the complexity for castlings in S.We show thatC(S)=1.Moreover,the MCbius function on S is calculated.And the Liouville functionCon S is studied.
