**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}*

**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^{s}m_{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.

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