Spectral properties of the M\'{o}bius function and a random M\'{o}bius model

Autor:	Abdalaoui, E. H. el, Disertori, M.
Rok vydání:	2013
Předmět:	Mathematics - Dynamical Systems 37A15 37A25 37A30
Druh dokumentu:	Working Paper
Popis:	Assuming Sarnak conjecture is true for any singular dynamical process, we prove that the spectral measure of the M\"{o}bius function is equivalent to Lebesgue measure. Conversely, under Elliott conjecture, we establish that the M\"{o}bius function is orthogonal to any uniquely ergodic dynamical system with singular spectrum. Furthermore, using Mirsky Theorem, we find a new simple proof of Cellarosi-Sinai Theorem on the orthogonality of the square of the M\"{o}bius function with respect to any weakly mixing dynamical system. Finally, we establish Sarnak conjecture for a particular random model. Comment: 24 pages, submitted for publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1305.4361 Zobrazit plný text záznamu View this record from Arxiv