Notes on the value distribution of ff^(k)-b

Abstract

Let f denote a transcendental meromorphic function with N(r, f) = S(r, f) and k be an integer. By using methods different from others, we have been able to derive several new results and pose some new conjectures that relate to the yet to be resolved conjecture concerning the quantitative estimates on the zeros of ff^(k)-b, for a non-vanishing small function b.