EVENT DETAILS AND ABSTRACT

Title: On the Ergodic Properties of Square-Free Numbers
Speaker: Francesco Cellarosi
Speaker Info: Princeton University
Brief Description:
Special Note:
Abstract:

We study binary and multiple correlations for the set of square-free numbers and we construct a dynamical systems naturally associated to them. We prove that this dynamical system has pure point spectrum and a classical result by von Neumann implies that it is isomorphic to a translation on a compact abelian group. In particular, the system is ergodic but not weakly mixing, and it has zero metric entropy. The latter results were announced recently by Peter Sarnak, and our method provides an alternative approach. Joint work with Yakov Sinai.