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A theorem in asymptotic number theory

Published online by Cambridge University Press:  09 April 2009

Jack P. Tull
Jack P. Tull
Affiliation:
The University of Adelaide, Australia and The Ohio State University, U.S.A.
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Let α(n) be a multiplicative arithmetic function. H. Delange [1] has proved that if |α(n)| ≦ 1 for all n and for a certain constant ρ, , where if ρ = 1 then then . He applied this result to several problems such as uniform distribution (mod 1) of certain types of sequences.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 2 , May 1965 , pp. 196 - 206
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Delange, H., Un théorè sur les fonctions arithmétiques multiplicatives et ses applications, Ann. scient. Éc. Norm. Sup. (3) 78 (1961), 1–29.Google Scholar
[2]Freud, G., Acta Math. Acad. Sci. Hungar. 2 (1951), 299–308.Google Scholar
[3]Karamata, J., Math. (Cluj) 4 (1930), 38–53.Google Scholar
[4]Korevaar, J., et al. , Nieuw Arch. Wiskunde 23 (1949), 77–86.Google Scholar