|Topic:||On the Ergodic Properties of Square-Free Numbers|
|Affiliation:||Member, School of Mathematics|
|Date:||Tuesday, December 6|
|Time/Room:||2:30pm - 3:30pm/S-101|
I shall explain the structure of correlation functions for square-free numbers and describe a 'natural' dynamical system associated to them. Spectral analysis allows us to show that this system is metrically isomorphic to a translation on a compact abelian group, and this fact has a number of dynamical consequences. These results are closely related to the recent work by P. Sarnak on the "Möbius randomness law". Joint work with Ya.G. Sinai.