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Multiplicative Functions Resembling the Mobius Function 被引量:1
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作者 Qing Yang LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第12期2316-2328,共13页
A multiplicative function f is said to be resembling the Mobius function if f is supported on the square-free integers,and f(p)=±1 for each prime p.We prove O-and Ω-results for the summatory function ∑_(n)≤x f... A multiplicative function f is said to be resembling the Mobius function if f is supported on the square-free integers,and f(p)=±1 for each prime p.We prove O-and Ω-results for the summatory function ∑_(n)≤x f(n)for a class of these f,and the point is that these O-results demonstrate cancellations better than the square-root saving.It is proved in particular that the summatory function is O(x^(1/3+ε))under the Riemann Hypothesis.On the other hand it is proved to be Ω(x^(1/4))unconditionally.It is interesting to compare these with the corresponding results for the Mobius function. 展开更多
关键词 mobius function random multiplicative function ZETA-function
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The Characteristic Polynomial of the Mixed Arrangement 被引量:2
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作者 SU Dan ZHANG Dunmu 《Wuhan University Journal of Natural Sciences》 CAS 2007年第2期203-206,共4页
We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arra... We consider the mixed arrangement which is composed of the central hyperplane arrangement and a sphere. We discuss the lattice of its intersection set and the relationship between the Mobius function of the mixed arrangement and the original hyperplane arangement. The Mobius function of the mixed arrangement is equal to the positive or the negative Mobius function of original hyperplane arrangement. Moreover, we give an equality of the chambers and the characteristic polynomial for the mixed arrangement. 展开更多
关键词 mixed arrangement mobius function characteristicpolynomial
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Q_(K) SPACES:A BRIEF AND SELECTIVE SURVEY 被引量:1
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作者 Guanlong BAO Hasi WULAN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期2039-2054,共16页
This article traces several prominent trends in the development of Mobius invariant function spaces Q_(K)with emphasis on theoretic aspects.
关键词 mobius invariant function spaces Q_(p) SPACES Q_(K) SPACES K-Carleson measures
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Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions
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作者 Kibrom G.EBREMESKEL Lin Zhe HUANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第8期1300-1310,共11页
In this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l^2(N,ω;). In particular, we focus on the operators M1 and Mμ, where μ, is the Mobius function. We investigate conditio... In this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l^2(N,ω;). In particular, we focus on the operators M1 and Mμ, where μ, is the Mobius function. We investigate conditions on the weight ω under which the operators M1 and Mμ are bounded. We show that for a positive and completely multiplicative function f,M1 is bounded on l^2(N, f^2) if and only if ||f||1 <∞, in which case ||M1||2,ω=||f||1, where ωn = f^2(n). Analogously, we show that Mμ is bounded on l^2(N, 1/n^2α) with ||M1||2,ω=ζ(α)/ζ(2α),where ωn= 1 /n^2α,α> 1. As an application, we obtain some results on the spectrum of M1^*M1 and M^*μMμ. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered. 展开更多
关键词 Arithmetic functions mobius function von Neumann algebra
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Sarnak’s Conjecture for Irregular Flows on Infinite-dimensional Torus 被引量:1
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作者 Qing Yang LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第9期1541-1548,共8页
Sarnak’s Disjointness Conjecture states that the Mobius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimension... Sarnak’s Disjointness Conjecture states that the Mobius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimensional torus. 展开更多
关键词 Sarnak's disjointness conjecture mobius function irregular flow skew product infinitedimensional torus
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Siegmund Duality for Continuous Time Markov Chains on Z_+~d
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作者 Pan ZHAO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第9期1460-1472,共13页
For the continuous time Markov chain with transition function P(t) on Z d + , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - (t). If Q, the q-m... For the continuous time Markov chain with transition function P(t) on Z d + , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - (t). If Q, the q-matrix of P(t), is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given. 展开更多
关键词 Continuous time Markov chains the Siegmund dual mobius function ↑-mobius mono-tonicity Feller Reuter Riley transition functions birth and death chains
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Hua’s theorem on five squares of primes
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作者 Wenjia ZHAO 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第4期835-850,共16页
We give an alternative proof of Hua’s theorem that each large N≡5(mod 24)can be written as a sum of five squares of primes.The proof depends on an estimate of exponential sums involving the Mobius function.
关键词 Exponential sums Hua's theorem mobius function
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