Derivatives of Meromorphic Functions with Multiple Zeros and Small Functions

Abstract EN

Let f z be a meromorphic function in ℂ , and let α z = R z h z ≢ 0 , where h z is a nonconstant elliptic function and R z is a rational function.

Suppose that all zeros of f z are multiple except finitely many and T r , α = o T r , f as r → ∞ .

Then f ' z = α z has infinitely many solutions.