Author Affiliation, Ana.
Department of Mathematics and Computer Science
Mean-value theorems of multiplicative functions on additive arithmetic semigroups
Date of Publication
In this paper, we consider additive arithmetical semigroups Ç of which the number Ç(n) of elements of degree n in Ç satisfies a general condition r G(n) = qnå Annrn-1 + O(qnn-g) n = 1 where r1< ... >rr and A1,...,Ar are arbitrary real constants, q >1, rr ³ 1, Ar > 0 and g > 1. We prove mean-value theorems for multiplicative functions on Ç, which are essentially best possible in some sense as their counterparts in classical probabilistic number theory. (AU)....