Defective functions of meromorphic functions in the unit disc

• Autorzy: Ciechanowicz E.

Identyfikatory

DOI

10.1515/jaa-2016-0002

• Języki publikacji: EN

Abstrakty

EN

Let f be a meromorphic function in the unit disc and (a_ν)^k_ν=1 a set of distinct meromorphic functions small with respect to f. An analogue of the second main theorem for f and (a_ν)^k_ν=1 is given. Upper limits for the sum of defects of an admissible meromorphic function and an admissible holomorphic function follow. For meromorphic and holomorphic functions in the unit disc and their small functions the analogues of Ullrich's theorem are presented.

Słowa kluczowe

EN

meromorphic function; holomorphic function; small functions; defect

PL

funkcja meromorficzna; funkcja holomorficzna; funkcja mała; defekt

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2016
• Tom: Vol. 22, nr 1
• Strony: 15--26
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Ciechanowicz E.

• Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

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• 5 I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.
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• 8 C. F. Osgood, Sometimes effective Thue–Siegel–Roth–Schmidt–Nevanlinna bounds, or better, J. Number Theory 21 (1985), 3, 347–389.
• 9 D. F. Shea and L. R. Sons, Value distribution theory for meromorphic functions of slow growth in the disc, Houston J. Math. 12 (1986), 2, 249–266.
• 10 N. Steinmetz, Eine Verallgemeinerung des zweiten Nevanlinnaschen Hauptsatzes, J. Reine Angew. Math. 368 (1986), 134–141.
• 11 M. Tsuji, Canonical product for a meromorphic function in a unit circle, J. Math. Soc. Japan 8 (1956), 1, 7–21.
• 12 E. Ullrich, Über die Ableitung einer meromorphen Funktion, Sitzungsberichte Akad. Berlin 1929 (1929), 592–608.
• 13 K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), 225–294.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.