On the distribution of complex-valued multiplicative functions
Let \(g_1,g_2\) be complex-valued multiplicative functions. The author finds a sufficient and necessary condition for \(g_1,g_2\) to have a joint limiting distribution. This is expressed in terms of sums involving \(u_g(p)= g(p)/ |g(p) |\) if \(g(p) \neq 0\), 0 if \(g(p)=0\) and \(v_g(p)=\log |g(p) |\) if \(|g(p) |\in(e^{-1},e)\) 1 otherwise. This result is less general than that of \textit{J.-L. Mauclaire} [Acta Arith. 68, 201-212 (1994; Zbl 0830.11029)], where the corresponding problem is solved in every locally compact commutative group, though the translation between them is not completely obvious because they are expressed in different terms.
scientific article; zbMATH DE number 912506
scientific article