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Uniqueness Problem of Meromorphic Mappings Sharing Moving Hyperplanes Regardless of Multiplicity

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Abstract

In this article, by giving a new method to estimate the counting functions of the auxiliary function, we prove a new uniqueness theorem for degenerate meromorphic mappings sharing moving hyperplanes regardless of multiplicity. Our result extends and improves almost all results in this topic.

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References

  1. Chen, Z., Li, Y., Yan, Q.: Uniqueness problem with truncated multiplicities of meromorphic mappings for moving targets. Acta Math. Sci. Ser. B Engl. Ed. 27, 625–634 (2007)

    Article  MathSciNet  Google Scholar 

  2. Nevanlinna, R.: Einige Eideutigkeitssätze in der Theorie der meromorphen Funktionen. Acta Math. 48, 367–391 (1926)

    Article  MathSciNet  Google Scholar 

  3. Noguchi, J., Ochiai, T.: Introduction to Geometric Function Theory in Several Complex Variables, Trans. Math. Monogr., vol. 80. American Mathematical Society, Providence (1990)

    Google Scholar 

  4. Quang, S.D.: Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem. Abh. Math. Semin. Univ. Hambg. 86, 1–18 (2016)

    Article  MathSciNet  Google Scholar 

  5. Quang, S.D.: Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings. Proc. Am. Math. Soc. 144, 4329–4340 (2016)

    Article  MathSciNet  Google Scholar 

  6. Quang, S.D.: Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions. Proc. Am. Math. Soc. 147, 1657–1669 (2019)

    Article  MathSciNet  Google Scholar 

  7. Quynh, L.N.: Algebraic dependences of meromorphic mappings sharing moving hyperplanes without counting multiplicities. Asian Eur. J. Math. 10(1), 1750040 (2017)

    Article  MathSciNet  Google Scholar 

  8. Ru, M.: A uniqueness theorem with moving targets without counting multiplicity. Proc. Am. Math. Soc. 129, 2701–2707 (2001)

    Article  MathSciNet  Google Scholar 

  9. Ru, M., Stoll, W.: The second main theorem for moving targets. J. Geom. Anal. 1, 99–138 (1991)

    Article  MathSciNet  Google Scholar 

  10. Thai, D.D., Quang, S.D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets. Int. J. Math. 16, 903–939 (2005)

    Article  MathSciNet  Google Scholar 

  11. Thai, D.D., Quang, S.D.: Second main theorem with truncated counting function in several complex variables for moving targets. Forum Mathematicum 20, 145–179 (2008)

    Article  MathSciNet  Google Scholar 

  12. Thoan, P.D., Duc, P.V., Quang, S.D.: Algebraic dependence and unicity theorem with a truncation level to 1 of meromorphic mappings sharing moving targets. Bull. Math. Soc. Sci. Math. Roum. 56(104), 513–526 (2013)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 101.04-2018.01.

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Correspondence to Si Duc Quang.

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Communicated by Filippo Bracci.

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Quang, S.D. Uniqueness Problem of Meromorphic Mappings Sharing Moving Hyperplanes Regardless of Multiplicity. Comput. Methods Funct. Theory 19, 659–669 (2019). https://doi.org/10.1007/s40315-019-00288-7

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  • DOI: https://doi.org/10.1007/s40315-019-00288-7

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