On the characterization of complex-valued multiplicative functions. II
[Part I, cf. ibid. 44, 401-406 (1984; Zbl 0562.10024).] The article contains the proof of the following theorem: Let \(f: {\mathbb{N}}\to {\mathbb{C}}\) be multiplicative. To any \(h: {\mathbb{N}}\to {\mathbb{R}}\) there exists a sequence \(A=\{a_ 1<a_ 2<...\}\), such that \(a_ n>h(n)\) and if at least two of the functions \(| f|\), Re f and Im f are monotonic on A, then \(f(n)=n^ k\) (except for some special cases).
characterization of complex-valued multiplicative functions
scientific article; zbMATH DE number 3908532