A new proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum. I
In 1929 F. Nevanlinna stated the following conjecture. Let f be a meromorphic function of finite order \(\rho\) with maximal deficiency sum: \[ \sum_{a\in {\bar {\mathbb{C}}}}\delta (a,f)=2. \] Then: 1) \(2\rho\) is a natural number \(\geq 2\). 2) If \(\delta (a)>0\), then \(\delta (a)=p(a)/\rho\), where p(a) is a natural number. 3) All the deficiency values are asymptotic. The complete proof of these statements has been obtained by \textit{D. Drasin} [Acta Math. 158, 1-94 (1987; Zbl 0622.30028)]. D. Drasin's proof was rather long and complicated. It makes use of a series of miscellaneous auxiliary tools. A. Eremenko found a new more accessible proof, based on the classical potential theory. Recently the method of the reviewed paper found new applications: the author and the reviewer proved ``a small function's'' version of the F. Nevanlinna conjecture in \textit{A. Eremenko} and \textit{M. Sodin} [Teor. Funkts. Funkts. Anal. Prilozh. (to appear)].
scientific article; zbMATH DE number 4190099