报告题目：On Chowla and Sarnak's conjectures for the Mobius flow

报告人：E. H. El Abdalaoui ,University of Rouen Normandy,  France

时间：3月28日（周三）下午 4：00-5：00

地点：数学科学学院 1518教室

摘要：The Liouville function λ is defined by 

λ(n) = (−1)Ω(n), for all n ∈ N∗

where Ω(n) is the number of prime factors of n counted with multiplicities with

Ω(1) = 1. the M¨obius function is given by μ(1) = 1, μ(n) = λ(n) if n is not

in the class of zero mod p2, for any prime number p, and zero otherwise.

In my talk, I will present my recent work on the connections between Chowla

and Sarnak’s conjectures. Roughly speaking, Chowla conjecture assert that the

Liouville function is normal and Sarnak conjecture assert that all dynamical

system with zero topological entropy satisfy the M¨obius randomness law. In

this talk, based on Veech’s proof of Sarnak’s theorem on the M¨obius flow

combined with logarithmic Tao’s theorem on Chowla and Sarnak’s conjectures,

I will establish that Chowla and Sarnak’s conjectures are equivalent.