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P-Adic Nevanlinna Theory Outside of a Hole

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Abstract

In this paper, we will establish the Nevanlinna theory for meromorphic functions outside a hole in \(\mathbb {K}\). We also give several applications of the theory to meromorphic functions out side a hole, such as results on branched values. Motzkin factors, known for analytic elements, play here an essential role.

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Acknowledgments

The second author is supported by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under grant number 101. 04-2014.41.

We are grateful to the referees for helpful comments and advices.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, 63000, Clermont-Ferrand, France

    Alain Escassut

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam

    Thi Hoai An Ta

  3. Institute of Mathematics and Applied Sciences (TIMAS), Thang Long University, Hanoi, Vietnam

    Thi Hoai An Ta

Authors
  1. Alain Escassut
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  2. Thi Hoai An Ta
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Correspondence to Alain Escassut.

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Escassut, A., Ta, T.H.A. P-Adic Nevanlinna Theory Outside of a Hole. Vietnam J. Math. 45, 681–694 (2017). https://doi.org/10.1007/s10013-017-0240-4

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  • DOI: https://doi.org/10.1007/s10013-017-0240-4

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