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ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS

Bhoosnurmath, Subhas S.;Kulkarni, Milind Narayanrao;Yu, Kit-Wing

  • Published : 2008.08.31

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 $\bar{d}$(P) and lower degree $\underline{d}$(P).

Keywords

differential polynomials;homogeneous;meromorphic functions;Nevanlinna theory;non-homogeneous;value distribution;zeros

References

  1. J. Clunie, On a result of Hayman, J. London Math. Soc. 42 (1967), 389-392 https://doi.org/10.1112/jlms/s1-42.1.389
  2. H. S. Gopalakrishna and S. S. Bhoosnurmath, On the deficiencies of differential polynomials, J. Karnatak Univ. Sci. 18 (1973), 329-335
  3. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964
  4. L. R. Son, Deficiencies of monomials, Math. Z. 111 (1969), 53-68 https://doi.org/10.1007/BF01110917
  5. C. C. Yang, On deficiencies of differential polynomials, Math. Z. 116 (1970), 197-204 https://doi.org/10.1007/BF01110073
  6. C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112 https://doi.org/10.1007/BF01110921
  7. L. Yang, Value Distribution Theory, Springer-Verlag, Berlin; Science Press, Beijing, 1993
  8. C. T. Chuang, On differential polynomials, Analysis of one complex variable (Laramie, Wyo., 1985), 12-32, World Sci. Publishing, Singapore, 1987
  9. W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9-42 https://doi.org/10.2307/1969890