On the value distribution of meromorphic functions in the punctured plane

A. Fernández

Some well-known facts of the value distribution theory for meromorphic functions in the plane will be considered in the punctured plane and also some results for entire functions will be extended to meromorphic functions in the plane with finitely many poles.

1. Bank S., Laine I. Representation of solutions of periodic second order linear differential equations// Journal für die Reine und Angewandte Mathematik. -- 1983. -- V.344. -- P. 1--21.

2. Bieberbach L. Theorie der Differentialgleichungen. -- Springer Verlag, Berlin, 1930.

3. Drasin D. Proof of a conjecture of F.Nevanlinna concerning functions which have deficiency sum two// Acta Mathematica. -- 1988. -- V.158. -- P. 1--94.

4. Hällström, G. Über meromorphe Funktionen mit mehrfach zusammenhängenden Existenzgebieten// Acta Academiae Aboensis. -- 1940. -- V.12, №8.

5. Hayman W.K. Meromorphic functions. -- Oxford Clarendon Press. 1964.

6. Korhonen R. Nevanlinna Theory in an annulus// Value distribution theory and related topics, Adv. Complex Anal. and Applic. Kluwer Academic Publishers. -- 2004. -- P. 167--179.

7. Khrystiyanin A.Ya., Kondrayuk A.A. On the Nevanlinna theory for meromorphic functions on annuli.~I// Mat. Stud. -- V.23, №1. -- P. 19--30.

8. Khrystiyanin A.Ya., Kondrayuk A.A. On the Nevanlinna theory for meromorphic functions on annuli.~II. // Mat. Stud. -- V.24, №1. -- P. 57--68.

9. Nevanlinna, R. Le théorème de Picard-Borel et la théorie de fonctions méromorphes. -- Chelsea Publishing Company, 1974.

10. Nevanlinna R. Analytic Functions. -- Springer Verlag, 1970.

11. Pfluger A. Zur Defektrelation ganzer Funktiones endlicher Ordnung // Commentarii Mathematici Helvetici.-- 1946. -- V.19. -- P. 91--104.

	On the value distribution of meromorphic functions in the punctured plane
Author	A. Fernández afernan@mat.uned.es Departamento de Matemáticas Fundamentales (UNED) Avenida de Senda del Rey, Nº 9 28040 Madrid, España
Abstract	Some well-known facts of the value distribution theory for meromorphic functions in the plane will be considered in the punctured plane and also some results for entire functions will be extended to meromorphic functions in the plane with finitely many poles.
Keywords	value distribution, meromorphic function, punctured plane
DOI	doi:10.30970/ms.34.2.136-144
Reference	1. Bank S., Laine I. Representation of solutions of periodic second order linear differential equations// Journal für die Reine und Angewandte Mathematik. -- 1983. -- V.344. -- P. 1--21. 2. Bieberbach L. Theorie der Differentialgleichungen. -- Springer Verlag, Berlin, 1930. 3. Drasin D. Proof of a conjecture of F.Nevanlinna concerning functions which have deficiency sum two// Acta Mathematica. -- 1988. -- V.158. -- P. 1--94. 4. Hällström, G. Über meromorphe Funktionen mit mehrfach zusammenhängenden Existenzgebieten// Acta Academiae Aboensis. -- 1940. -- V.12, №8. 5. Hayman W.K. Meromorphic functions. -- Oxford Clarendon Press. 1964. 6. Korhonen R. Nevanlinna Theory in an annulus// Value distribution theory and related topics, Adv. Complex Anal. and Applic. Kluwer Academic Publishers. -- 2004. -- P. 167--179. 7. Khrystiyanin A.Ya., Kondrayuk A.A. On the Nevanlinna theory for meromorphic functions on annuli.~I// Mat. Stud. -- V.23, №1. -- P. 19--30. 8. Khrystiyanin A.Ya., Kondrayuk A.A. On the Nevanlinna theory for meromorphic functions on annuli.~II. // Mat. Stud. -- V.24, №1. -- P. 57--68. 9. Nevanlinna, R. Le théorème de Picard-Borel et la théorie de fonctions méromorphes. -- Chelsea Publishing Company, 1974. 10. Nevanlinna R. Analytic Functions. -- Springer Verlag, 1970. 11. Pfluger A. Zur Defektrelation ganzer Funktiones endlicher Ordnung // Commentarii Mathematici Helvetici.-- 1946. -- V.19. -- P. 91--104.
Pages	136-144
Volume	34
Issue	2
Year	2010
Journal	Matematychni Studii
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