An Omega Theorem for a Class of Arithmetic Functions

This paper deals with the average order of arithmetic functions a(n) with a generating function of the shape (1.1) where fk and gj possess certain characteristic properties of the zera‐function. Under fairly general conditions, a lower bound for the error term in the asymptotic formula for the corresponding Dirichlet summatory function is established. Finally, several specific applications to functions from elementary number theory and to arithmetic problems in number fields are discussed.