Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  419.10006
Autor:  Erdös, Paul; Hall, R.R.
Title:  On the Möbius function. (In English)
Source:  J. Reine Angew. Math. 315, 121-126 (1980).
Review:  The function M(n,T) = sum{\mu(d): d| n,d \leq T} is studied in this paper. It is shown that M(n,T) is usually zero, in two senses. First, the density of the integers n such that M(n,T)\ne0 tends to zero as a function of T. Second, as previously conjectured by Erdös, for almost all n we have sum{1/T: M(n,T)\ne0} = o(log n]. Both results are given in precise quantitative form, and are shown to be connected with other conjectures and unsolved problems, in particular with Erdös' conjecture that almost all integers n have two divisions d,d' such that d < d' < 2d.
Classif.:  * 11A25 Arithmetic functions, etc.
                   11N05 Distribution of primes
Keywords:  Möbius function; density

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