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On the value distribution of differential polynomials
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In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree d (P) and lower degree d (P).
Abstract
In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree d (P) and lower degree d (P).
참고문헌 (9)
- C. T. Chuang, "On differential polynomials, Analysis of one complex variable (Laramie, Wyo., 1985)", pp.12~32 (1987), World Sci. Publishing
- J. Clunie, "On a result of Hayman", Journal of the London Mathematical Society, 42, pp.389~392 (1967)
- H. S. Gopalakrishna, "On the deficiencies of differential polynomials", Karnatak University Journal Science, 18, pp.329~335 (1973)
- W. K. Hayman, "Meromorphic Functions" (1964), Oxford Mathematical Monographs Clarendon Press
- W. K. Hayman, "Picard values of meromorphic functions and their derivatives", Annals of Mathematics, 70, pp.9~42 (1959)
- L. R. Son, "Deficiencies of monomials", Mathematische Zeitschrift, 111, pp.53~68 (1969)
- C. C. Yang, "On deficiencies of differential polynomials", Mathematische Zeitschrift, 116, pp.197~204 (1970)
- C. C. Yang, "On deficiencies of differential polynomials II", Mathematische Zeitschrift, 125, pp.107~112 (1972)
- L. Yang, "Value Distribution Theory" (1993), Springer-Verlag, Berlin; Science Press
관련 논문AI추천
A note on the value distribution of differential polynomialsBikash Chakraborty, Hari M. Srivastava, Subhas S. Bhoosnurmath대한수학회 · 대한수학회논문집2019 · 제34권 제4호ON DEFICIENCIES OF CERTAIN HOMOGENEOUS DIFFERENTIAL POLYNOMIALSHARINA P.WAGHAMORE장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제3호Zero distribution of some delay-differential polynomialsIlpo Laine, Zinelaabidine Latreuch대한수학회 · 대한수학회보2020 · 제57권 제6호Growth of solutions of non-homogeneous linear differential equations and its applicationsDilip Chandra Pramanik, Manab Biswas강원경기수학회 · 한국수학논문집2021 · 제29권 제1호On exceptional values of homogeneous differential polynomialsH. P. Waghamore, Subhas S. Bhoosnurmath장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2007 · 제10권 제2호Value Distribution of the Product of a Meromorphic Derivative and a Power of the FunctionIndrajit Lahiri, Rajib Mukherjee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제2호
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