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Sur les fonctions multiplicatives complexes de module \(\leq 1\). (On complex valued multiplicative functions with absolute value \(\leq 1\)). (French) Zbl 0884.11035
Summary: The author gives detailed proofs of results that he had announced previously [H. Delange, C. R. Acad. Sci., Paris, Sér. A 276, 161-164 (1973; Zbl 0245.10043)] concerning the behaviour as \(N\) tends to infinity of the distribution of the values on the integers from 1 to \(N\) of a complex multiplicative function of absolute value \(\leq 1\). He adds some remarks not contained in the original paper.

MSC:
11K65 Arithmetic functions in probabilistic number theory
11N64 Other results on the distribution of values or the characterization of arithmetic functions
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References:
[1] H. DELANGE, Sur LES fonctions arithmétiques multiplicatives, Ann. Sci. Ecole Norm. Sup, (3) 78 (1961), 273-304. · Zbl 0234.10043
[2] H. DELANGE, On the distribution modulo 1 of additive functions, J. Indian Math. Soc. (N.S.), 34 (1970), 215-235. · Zbl 0234.10044
[3] H. DELANGE, Sur la distribution des valeurs des fonctions multiplicatives complexes, C. R. Acad. Sci. Paris, série A, 276 (1973), 161-164. · Zbl 0245.10043
[4] G. HALÁSZ, Über die mittelwerte multiplikativer zahlentheoretischer funktionen, Acta Math. Acad. Sci. Hungar., 19 (1968), 365-403. · Zbl 0165.05804
[5] E. WIRSINGDas asymptotische verhalten von summen über multiplikativer funktionen II, Acta Math. Acad. Sci. Hungar., 18 (1967), 411-467. · Zbl 0165.05901
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