Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 603-619

ON DEVIATIONS, DEFECTS AND ASYMPTOTIC FUNCTIONS OF MEROMORPHIC FUNCTIONS

Liudmyla Kaluzhynova and Ivan Marchenko

Kharkiv National University, Department of Mathematics
Svobody sq. 4, Kharkiv, 61077, Ukraine; kaluzhynova 'at' univer.kharkov.ua

University of Szczecin, Institute of Mathematics
ul. Wielkopolska 15, 70-451 Szczecin, Poland; marchenko 'at' wmf.univ.szczecin.pl

Abstract. The structure of the set of deviations b(q,f) of meromorphic functions with N(r,f) = o(T(r,f)) from rational functions is investigated. A sharp estimate for the sum of these quantities is obtained. Also we investigated the structure of the set of deviations b(q,f) of meromorphic functions from polynomials. We applied the obtained results to the study of strong asymptotic values of meromorphic functions.

2010 Mathematics Subject Classification: Primary 30D35; Secondary 30D30.

Key words: Meromorphic function, deviation, asymptotic function.

Reference to this article: L. Kaluzhynova and I. Marchenko: On deviations, defects and asymptotic functions of meromorphic functions. Ann. Acad. Sci. Fenn. Math. 36 (2011), 603-619.

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doi:10.5186/aasfm.2011.3638