Derivatives of Meromorphic Functions with Multiple Zeros and Small Functions

Abstract

Let fz be a meromorphic function in ℂ, and let αz=Rzhz≢0, where hz is a nonconstant elliptic function and Rz is a rational function. Suppose that all zeros of fz are multiple except finitely many and Tr,α=oTr,f as r→∞. Then f'z=αz has infinitely many solutions.