LASZLO TOTH

Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, VIII. On the product and the quotient of s_{A, s} and f_{A, s}

Pages: 199-206
Received: 18 February 1999   
Mathematics Subject Classification: 11A25 - 11N37

Abstract: Let A be a regular convolution of Narkiewicz type, s_A,s (n) denote the sum of s-th powers of A-divisors of n and let
f_{A, s} (n) = å_{d ÎA(n)} d^sm_A(n/d) be the generalized Euler function. In this paper we establish asymptotic formulae for
å _n£x s_A,s (n)f_A,s (n) , å _n£x s_A,s (n)/f_A,s (n) , in case s > 0 and for å_{n £x} f_A,s (n)/s_{A, s} (n) in case s³1, assuming that A is a cross-convolution, investigated in our previous papers.