The Möbius function and statistical mechanics

F. Cellarosi, Ya G. Sinai

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider a probabilistic model for square-free numbers, and provide limit theorems for several random variables defined in our ensemble. The limit transition corresponds to the thermodynamical limit in Statistical Mechanics. We also prove some inequalities inspired by a recent conjecture by P. Sarnak concerning the randomness in the Möbius sequence, and discuss a method of summation for the Riemann zeta function ζ(s) on the vertical line Rs = 1.

Original languageEnglish (US)
Pages (from-to)245-275
Number of pages31
JournalBulletin of Mathematical Sciences
Volume1
Issue number2
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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