On the second fundamental theorem of Nevanlinna

Fernández Arias, Arturo

doi:10.1090/S0002-9947-1988-0927686-6

On the second fundamental theorem of Nevanlinna
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Trans. Amer. Math. Soc. 306 (1988), 141-163 Request permission

Abstract:

It is shown that a condition on the size of the exceptional set in the second fundamental theorem of Nevanlinna cannot be improved. The method is based on a construction of Hayman and also makes use of a quantitative version of a result of F. Nevanlinna about the growth of the characteristic function of a meromorophic function omitting a finite number of points

References

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Le théorème de Picard-Borel et la théorie des fonctions méromorphes

Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280, DOI 10.1007/978-3-642-85590-0