摘要
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.
基金
Tianyuan Mathematical Center in Southwest(No.11826102)
supported by NSFC grant(Nos.12090012,12031019,12090010)
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 province
supported 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.
