The Möbius function and statistical mechanics

F. Cellarosi; Ya G. Sinai

doi:10.1007/s13373-011-0011-6

The Möbius function and statistical mechanics

F. Cellarosi, Ya G. Sinai

Research output: Contribution to journal › Article › peer-review

7 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 language	English (US)
Pages (from-to)	245-275
Number of pages	31
Journal	Bulletin of Mathematical Sciences
Volume	1
Issue number	2
DOIs	https://doi.org/10.1007/s13373-011-0011-6
State	Published - Jan 1 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s13373-011-0011-6

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AB - 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.

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The Möbius function and statistical mechanics

Abstract

All Science Journal Classification (ASJC) codes

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