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A note on the Bruck conjecture

Feng Lu
대한수학회 (The Korean Mathematical Society)|2011.09|대한수학회보 (Bulletin of the KMS)|제48권 제5호|pp. 951-957

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참고문헌

키워드

uniquenessnormal familyNevanlinna theoryentire functions
주제분류수학

초록

In 1996, Bruck studied the relation between f and f' if an entire function f shares one value a CM with its first derivative f' and posed the famous Bruck conjecture. In this work, we generalize the value a in the Bruck conjecture to a small function α. Meanwhile, we prove that the Bruck conjecture holds for a class of meromorphic functions.

Abstract

In 1996, Bruck studied the relation between f and f' if an entire function f shares one value a CM with its first derivative f' and posed the famous Bruck conjecture. In this work, we generalize the value a in the Bruck conjecture to a small function α. Meanwhile, we prove that the Bruck conjecture holds for a class of meromorphic functions.

참고문헌 (16)

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  6. W. Hayman, "Meromorphic Functions" (1964), Clarendon Press
  7. X. J. Liu, "On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1", J. Math. Anal. Appl, 348(1), pp.516~529 (2008)
  8. F. Lu, "Entire functions sharing polynomials with their first derivatives", Arch. Math. (Basel), 92(6), pp.593~601 (2009)
  9. F. Lu, "On the uniqueness problems of meromorphic functions and their linear differential polynomials", J. Math. Anal. Appl, 362(2), pp.301~312 (2010)
  10. E. Mues, "Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen", Manuscripta Math, 29(2), pp.195~206 (1979)
  11. L. A. Rubel, "Values shared by an entire function and its derivative, Complex analysis", Proc. Conf, pp.101~103 (1976), Univ. Kentucky
  12. J. Wang, "Uniqueness theory of entire functions that share a small function with its differential polynomails", Indian J. Pure Appl. Math, 35, pp.1119~1129 (2004)
  13. C. C. Yang, "The uniqueness theory of meromorphic functions, Mathematics and Its Applications", pp.2003, Science Press
  14. L. Z. Yang, "Non-existence of meromorphic solutions of a Fermat type functional equation", Aequationes Math, 76(1), pp.140~150 (2008)
  15. J. L. Zhang, "Some results related to a conjecture of R. Bruck concerning meromorphic functions sharing one small function with their derivatives", Ann. Acad. Sci. Fenn. Math, 32(1), pp.141~149 (2007)
  16. J. L. Zhang, "A power of a meromorphic function sharing a small function with its derivative", Ann. Acad. Sci. Fenn. Math, 34(1), pp.249~260 (2009)

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