On the distribution of complex-valued multiplicative functions

Laurinčikas, Antanas

Laurinčikas, Antanas

Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 183-203.

Résumé
Abstract

Soient $g_{1} (m), g_{2} (m)$ deux fonctions multiplicatives a valeurs complexes. Dans un article on donne les conditions nécessaires et suffisantes de la convergence en un certain sens de

\frac{1}{n} N_{n} ((g_{1} (m), g_{2} (m)) \in A), A \in ℬ (ℂ^{2}),

quand

n \to \infty .

Let $g_{j} (m), j = 1, 2$ , be complex-valued multiplicative functions. In the paper the necessary and sufficient conditions are indicated for the convergence in some sense of probability measure

\frac{1}{n} card \{0 \leq m \leq n : (g_{1} (m), g_{2} (m)) \in A\}, A \in ℬ (ℂ^{2}),

n \to \infty

MR Zbl

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     author = {Laurin\v{c}ikas, Antanas},
     title = {On the distribution of complex-valued multiplicative functions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {183--203},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {1},
     year = {1996},
     mrnumber = {1399954},
     zbl = {0864.11039},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1996__8_1_183_0/}
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Laurinčikas, Antanas. On the distribution of complex-valued multiplicative functions. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 183-203. http://www.numdam.org/item/JTNB_1996__8_1_183_0/

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