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Two linear polynomials shared by an entire function and its linear differential polynomials

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In this paper, we study a uniqueness problem of entire functions that share two linear polynomials with its linear differential polynomial. We deduce two theorems which improve some previous results given by I. Lahiri \cite{5}.

Abstract

In this paper, we study a uniqueness problem of entire functions that share two linear polynomials with its linear differential polynomial. We deduce two theorems which improve some previous results given by I. Lahiri \cite{5}.

참고문헌 (13)

  1. C. A. Berenstein, "On the shared values of entire functions and their partial differential polynomials in Cn", Forum Math, 8(3), pp.379~396 (1996)[DOI]
  2. G. Frank, "Lecture notes on sharing values of entire and meromorphic functions", Workshops in Complex Analysis (1991)
  3. Y. X. Gu, "Uniqueness of an entire function and its differential polynomial", Acta Math. Sinica, 37(6), pp.791~798 (1994)
  4. W. K. Hayman, "Meromorphic Functions, Oxford Mathematical Monographs" (1964), Clarendon Press
  5. I. Lahiri, "Weighted sharing and uniqueness of meromorphic functions", Nagoya Math. J, 161, pp.193~206 (2001)[DOI]
  6. I. Lahiri, "Weighted value sharing and uniqueness of meromorphic functions", Complex Var. Theory Appl, 46(3), pp.241~253 (2001)[DOI]
  7. I. Lahiri, "An entire function sharing two values with its linear differential polynomial", Bull. Aust. Math. Soc, 97(2), pp.265~273 (2018)[DOI]
  8. P. Li, "Value sharing of an entire function and its derivatives", J. Math. Soc. Japan, 51(4), pp.781~799 (1999)[DOI]
  9. P. Li, "When an entire function and its linear differential polynomial share two values", Illinois J. Math, 44(2), pp.349~362 (2000)[DOI]
  10. E. Mues, "Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen", Manuscripta Math, 29(2-4), pp.195~206 (1979)[DOI]
  11. L. A. Rubel, "Values shared by an entire function and its derivative, in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976)", Lecture Notes in Math, 599, pp.101~103 (1977), Springer
  12. L. Z. Yang, "Entire functions that share finite values with their derivatives", Bull. Austral. Math. Soc, 41(3), pp.337~342 (1990)[DOI]
  13. C. -C. Yang, "Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557" (2003), Kluwer Academic Publishers Group

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