On the Ergodic Properties of Square-Free Numbers
| Analysis Seminar | |
| Topic: | On the Ergodic Properties of Square-Free Numbers |
| Speaker: | Francesco Cellarosi |
| 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.