Uniqueness of admissible meromorphic functions in the unit disc
Let \(f(z)\) be a meromorphic function in the unit disc \(D\) such that \(\limsup_{r\to 1}(T(r,f)/\log(1/1-r))=+\infty\). Such a function is called admissible in this article. As is well-known, the classical five-point and four-point uniqueness theorems for meromorphic functions in the plane permit a large collection of variants and generalizations. This article proves a number of corresponding uniqueness theorems for admissible meromorphic functions in the unit disc. The proofs make extensive use of the Nevanlinna theory in the unit disc; the reasoning closely follows the corresponding argumentation in the plane. It would be interesting to know which results from the plane don't carry over to the unit disc: The final remark in this article offers such an example.
scientific article; zbMATH DE number 1342684