Oscillatory properties of arithmetical functions. I (Q1088715)

The authors investigate the function V(f,Y), the number of sign changes of f(x) in the interval (0,Y) where certain conditions are imposed on f. Results about V(f,y) have been obtained by Landau, Polya, and Grosswald. The purpose of this paper is to prove a counterpart result to the theorem of Grosswald in which lim sup is replaced by lim inf. A corollary of the result is sharpening of Polya's theorem which can be applied to the partial sums of many number-theoretic functions.