On the distribution of \(q\)-additive functions. (Sur la répartition des fonctions \(q\)-additives.) (French) Zbl 0788.11032

Let \(f\) be a \(q\)-additive function with values in a metrizable locally compact commutative group \(G\). A necessary and sufficient condition is found for \(f\) to have a limiting distribution with a suitable centering; in particular, it is proved that for a compact group, such a centering always exists. Also a necessary and sufficient condition is found for the continuity of the limiting distribution when it exists.


11K65 Arithmetic functions in probabilistic number theory
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