PIMS/ UBC Distinguished Colloquium: Yakov Sinai

In this talk I shall discuss the results which were obtained by several people: M.Avdeeva, F.Cellarosi, Dong Li and myself. Moebius function is one of the most important functions in number theory also connected with Riemann hypothesis. Its simplest part leads to the well-known in probability theory Dickman-de Bruijn distribution. The so-called Mirsky formulas allow to construct the dynamical system with pure point spectrum corresponding to the square of the Moebius function. In the last part of the talk the famous Hall theorem about the variance of the number of square-free numbers will be discussed.