A proximity property of the $a$-points of meromorphic functions

The author establishes a new property of the distribution of the $a$-points of all functions that are meromorphic in $\mathbf C$. This is a “proximity” property of the sets of $a$-points for “most” values $a\in\overline{\mathbf C}$. It turns out that this regularity of the distribution of the $a$-points leads to sharper forms of the deficiency relations of Nevanlinna and Ahlfors. The proof depends on Ahlfors' theory of covering surfaces.
Figures: 3.
Bibliography: 7 titles.