AN OMEGA THEOREM FOR A CLASS OF ARITHMETIC FUNCTIONS

This paper deals with the average order of arithmetic functions a(n) w ith a generating function of the shape (1.1) where f(k) and g(j) posse ss certain characteristic properties of the zera-function. Under fairl y general conditions, a lower bound for the error term in the asymptot ic formula for the corresponding Dirichlet summatory function is estab lished. Finally, several specific applications to functions from eleme ntary number theory and to arithmetic problems in number fields are di scussed.