Remarks on an elementary proof of Halász's theorem
A fundamental theorem of \textit{G. Halász} [Acta Math. Acad. Sci. Hung. 19, 365-403 (1968; Zbl 0165.058)] describes those multiplicative functions that satisfy \(|f(n) |\leq 1\) and have a mean value. \textit{H. Daboussi} and the author [Math. Z. 209, 43-52 (1992; Zbl 0736.11053)] gave a new proof of this result. Here a part of this proof is simplified. It should be noted that this proof is not completely `elementary' in the usual sense: complex functions are applied, though definitely less heavily than in the classical `analytical' proof.
scientific article; zbMATH DE number 794499
scientific article