Contributions to Analytic Number Theory

This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on analytic number theory. They concern weighted inversion theorems of the Wiener type, mean-value theorems for multiplicative functions, and, Ramanujan expansions.Mathematics Subject Classification (1991): 11A25, 11N37 Keywords: analytic number theory, arithmetic functions, related numbers, inversion formulas, Dirichlet algebras, arithmetic semigroups, weighted inversion theorems, semigroup, John Knopfmacher, analytic number theory, number theory, multiplicative function, Ramanujan expansions, expansions Quaestiones Mathematicae 24(3) 2001, 309-32