Relations between the Growths of an Increasing f(x) and fz f(t)lt dt and Applications to Entire Functions

Abstract

Let P (z) be a non-constant entire function throughout and let, as usual (Ch. II of [1]), the functions M(r:P) and n (r:P) be the maximum modulus and the counting function of the zeros of P and let μ (r : P) and v (r : P) be the maximum term and its rank, associated with the Maclaurin Expansion of P.