Conditional asymptotic formulae for a class of arithmetic functions

Abstract

Under the assumption of Riemann’s Hypothesis, a general asymptotic formula for sums ∑ n ≤ x a ( n ) \sum \nolimits _{n \leq x} {a\left ( n \right )} is established which applies (e.g.) to arithmetic functions a ( n ) a\left ( n \right ) defined by a kind of convolution of the Möbius function with some divisor function.