Functiones et Approximatio Commentarii Mathematici

On some arithmetical multiplicative functions

Jean-Loup Mauclaire

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Abstract

We characterize some non-negative multiplicative functions $f(n)$ such that $\lim_{x\rightarrow +\infty}\frac{1}{x}\sum_{{1\leq n\leq x }\atop {n\in A }} f(n)$ exists and is positive, but there exists a subset $A(f)$ of $N$ of density $1$ such that $\lim_{x\rightarrow +\infty }\frac{1}{x}\sum_{{1\leq n\leq x }\atop {n\in A(f)}} f(n)=0$. An application to the case of the Ramanujan $\tau$-function is provided.

Article information

Source
Funct. Approx. Comment. Math., Volume 35 (2006), 219-233.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229442625

Digital Object Identifier
doi:10.7169/facm/1229442625

Mathematical Reviews number (MathSciNet)
MR2271615

Zentralblatt MATH identifier
1196.11135

Subjects
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions 11N56: Rate of growth of arithmetic functions

Keywords
mean-value multiplicitive functions

Citation

Mauclaire, Jean-Loup. On some arithmetical multiplicative functions. Funct. Approx. Comment. Math. 35 (2006), 219--233. doi:10.7169/facm/1229442625. https://projecteuclid.org/euclid.facm/1229442625


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