Contributions to Analytic Number Theory

Abstract

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, 309-322