On an Identity Theorem in the Nevanlinna Class N Original Research Article

We prove the following theorem: Let ƒ be in the Nevanlinna class N, and let zn be distinct points in the unit disk D with Σ∞n=1 (1 - |zn|) = ∞. Further let λn > 0, λn → ∞ as n → ∞ and ϵn > 0, Σ∞n=1 ϵn < ∞. If [formula] where [formula] then ƒ ≡ 0. This result is an extension of the classical theorem of Blaschke about the zeros of functions in the Nevanlinna class N, in the case when these zeros are distinct.