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Vietnam Journal of Mathematics

, Volume 45, Issue 4, pp 681–694 | Cite as

P-Adic Nevanlinna Theory Outside of a Hole

  • Alain EscassutEmail author
  • Thi Hoai An Ta
Article

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.

Keywords

P-adic meromorphic functions Nevanlinna’s theory Values distribution Small functions Picard values Branched values 

Mathematics Subject Classification (2010)

12J25 30D35 30G06 46S10 

Notes

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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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Blaise PascalUniversité Clermont AuvergneClermont-FerrandFrance
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  3. 3.Institute of Mathematics and Applied Sciences (TIMAS)Thang Long UniversityHanoiVietnam

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