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On Uniqueness of Meromorphic Functions Sharing Finite Sets

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Proceedings of the Second ISAAC Congress

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 7))

Abstract

In this article, we first study polynomials P(w) such that P(f) = cP(g) implies f = g for any nonzero constant c and nonconstant meromorphic functions f and g on ℂ. Next, we give some sufficient conditions for a finite set S to be a uniqueness range set, namely, to satisfy the condition that f -1(S) = g -1(S) implies f = g for any nonconstant meromorphic functions f and g on ℂ.

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References

  1. S. Bartels, Meromorphic functions sharing a set with 17 elements ignoring multiplicities, preprint.

    Google Scholar 

  2. G. Frank and M. Reinders, A unique range set for meromorphic functions with 11 elements, Complex Var. Theory Appl.. 37(1998), 185–193.

    MathSciNet  MATH  Google Scholar 

  3. H. Fujimoto, Value distribution theory of the Gauss map of minimal surfaces, Aspect of Math, Vol. E21, Vieweg, Wiesbaden, 1993.

    MATH  Google Scholar 

  4. F. Gross and C.C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. 58(1982), 17–20.

    MathSciNet  MATH  Google Scholar 

  5. P. Li and C.C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J., 18(1995), 437–450.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math., 48(1926), 367–391.

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Shiffman, Uniqueness of entire and meromorphic functions sharing finite sets, unpublished.

    Google Scholar 

  8. C.C. Yang and X. Hua, Unique polynomials of entire and meromorphic functions, Matematicheskaya fizika, analiz, geometriya, 3(1997), 391–398.

    MathSciNet  Google Scholar 

  9. H. Yi, The unique range sets of entire or meromorphic functions, Complex Var. Theory Appl., 28(1995), 13–21.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathemathematics Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan

    Hirotaka Fujimoto

Authors
  1. Hirotaka Fujimoto
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Editor information

Editors and Affiliations

  1. Freie Universität, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, Delaware, USA

    Robert P. Gilbert

  3. Kyushu University, Fukuoka, Japan

    Joji Kajiwara

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© 2000 Kluwer Academic Publishers

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Fujimoto, H. (2000). On Uniqueness of Meromorphic Functions Sharing Finite Sets. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0269-8_34

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  • DOI: https://doi.org/10.1007/978-1-4613-0269-8_34

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7970-6

  • Online ISBN: 978-1-4613-0269-8

  • eBook Packages: Springer Book Archive

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