On the order of the difference of two meromorphic functions

Abstract

THEOREM A. Let f(z) = Pi(z) exp(Qi(z)) P2(z) exp(Q2(Z)) * 0 where Qi(z) and Q2(z) are polynomials of degree p (p being an integer) and Pi(z), P2(z) are canonical products of order ArP where A is some suitable constant; M(r, f) being max If(z) I for |zj =r. In this note we prove the following extension of Theorem A. THEOREM 1. Let Pi(z), i = 1, 2, 3, 4 be canonical products or polynomials (not having any zero at origin) or constants (neither zero nor infinity) such that P1 and P3 have no common zeros, P2 and P4 have no common zeros, and let p be a positive integer and (1.1) -nlim sup T(,1, Pi)/rP = at < ??o r *