ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS

Title & Authors
ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS
Bhoosnurmath, Subhas S.; Kulkarni, Milind Narayanrao; Yu, Kit-Wing;

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 $\small{\bar{d}}$(P) and lower degree $\small{\underline{d}}$(P).
Keywords
differential polynomials;homogeneous;meromorphic functions;Nevanlinna theory;non-homogeneous;value distribution;zeros;
Language
English
Cited by
References
1.
C. T. Chuang, On differential polynomials, Analysis of one complex variable (Laramie, Wyo., 1985), 12-32, World Sci. Publishing, Singapore, 1987

2.
J. Clunie, On a result of Hayman, J. London Math. Soc. 42 (1967), 389-392

3.
H. S. Gopalakrishna and S. S. Bhoosnurmath, On the deficiencies of differential polynomials, J. Karnatak Univ. Sci. 18 (1973), 329-335

4.
W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964

5.
W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9-42

6.
L. R. Son, Deficiencies of monomials, Math. Z. 111 (1969), 53-68

7.
C. C. Yang, On deficiencies of differential polynomials, Math. Z. 116 (1970), 197-204

8.
C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112

9.
L. Yang, Value Distribution Theory, Springer-Verlag, Berlin; Science Press, Beijing, 1993