Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, VIII. On the product and the quotient of sA, s and fA, s
Received: 18 February 1999
Mathematics Subject Classification: 11A25 - 11N37
Let A be a regular convolution of Narkiewicz type,
(n) denote the sum of s-th powers of A-divisors of n and let
fA, s (n) = åd ÎA(n) dsmA(n/d) be the generalized Euler function. In this paper we establish asymptotic formulae for
å n£x sA,s (n)fA,s (n) , å n£x sA,s (n)/fA,s (n) , in case s > 0 and for ån £x fA,s (n)/sA, s (n) in case s³1, assuming that A is a cross-convolution, investigated in our previous papers.