Geodesic
A proximity property of the $a$-points of meromorphic functions
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 41-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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G. A. Barsegyan. A proximity property of the $a$-points of meromorphic functions. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 41-63. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a2/

[1] Nevanlinna R., Odnoznachnye analiticheskie funktsii, OGIZ, M., 1941

[2] Barsegyan G. A., “Novye rezultaty v teorii meromorfnykh funktsii”, DAN SSSR, 238:4 (1978), 777–780 | MR | Zbl

[3] Barsegyan G. A., “O geometrii meromorfnykh funktsii”, Matem. sb., 114 (156) (1981), 179–225 | MR | Zbl

[4] Dufresnoy J., “Sur les domaines couvertes par les valeurs d'une fonction meromorphe ou algebroide”, Ann. Sci. Ecole Norm. Sup., (3), 58, 1941, 179–259 | MR | Zbl

[5] Kheiman U. K., Meromorfnye funktsii, Mir, M., 1966 | MR

[6] Miles J., “A note on Ahlfors' theory of covering surfaces”, Proc. Amer. Math. Soc, 21:1 (1969), 30–32 | DOI | MR | Zbl

[7] Gyzha B. O., “Zamechanie k teorii Alforsa nakryvayuschikh poverkhnostei”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, 20 (1974), 70–72 | Zbl