Skip to main content
SpringerLink
Log in

Algebraic Dependences of Three Meromorphic Mappings Sharing Few Moving Hyperplanes

  • Published:
Acta Mathematica Vietnamica Aims and scope Submit manuscript

Abstract

In this article, some algebraic dependence theorems for three meromorphic mappings into a projective space sharing few moving hyperplanes are given. Our results are improvements of many previous results in this topic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, Z., Yan, Q.: Uniqueness theorem of meromorphic mappings into PN(C) sharing 2N + 3 hyperplanes regardless of multiplicities. Internat. J. Math. 20(6), 717–726 (2009)

    Article  MathSciNet  Google Scholar 

  2. Chen, Z., Ru, M.: A uniqueness theorem for moving targets with truncated multiplicities. Houst. J. Math. 32(2), 589–601 (2006)

    MathSciNet  MATH  Google Scholar 

  3. 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(3), 625–634 (2007)

    MathSciNet  MATH  Google Scholar 

  4. Fujimoto, H.: Uniqueness problem with truncated multiplicities in value distribution theory. Nagoya Math. J. 152, 131–152 (1998)

    Article  MathSciNet  Google Scholar 

  5. Quang, S.D.: Algebraic dependences of meromorphic mappings sharing few moving hyperplanes. Ann. Polon. Math. 108(1), 61–73 (2013)

    Article  MathSciNet  Google Scholar 

  6. Quang, S.D., Giang, H.H.: A finiteness theorem for meromorphic mappings sharing few moving hyperplanes. Vietnam J. Math. 43(4), 725–742 (2015)

    Article  MathSciNet  Google Scholar 

  7. 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), 1–18 (2016)

    Article  MathSciNet  Google Scholar 

  8. Quang, S.D.: Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings. Proc. Am. Math. Soc. 144(10), 4329–4340 (2016)

    Article  MathSciNet  Google Scholar 

  9. Quang, S.D.: Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions. Proc. Am. Math. Soc. https://doi.org/10.1090/proc/14377, arXiv:1806.01647 [math.CV] (2018)

  10. Quang, S.D.: Degeneracy and finiteness theorems for meromorphic mappings in several complex variables. Chin. Ann. Math. Ser. B 40(2), 251–272 (2019)

    Article  MathSciNet  Google Scholar 

  11. Quynh, L.N.: Algebraic dependences of meromorphic mappings sharing moving hyperplanes without counting multiplicities. Asian-Eur. J. Math. 10(3), 1750040, 15 (2017)

    Article  MathSciNet  Google Scholar 

  12. Ru, M.: A uniqueness theorem with moving targets without counting multiplicity. Proc. Am. Math. Soc. 129(9), 2701–2707 (2001)

    Article  MathSciNet  Google Scholar 

  13. Ru, M., Wang, J.T.-Y.: Truncated second main theorem with moving targets. Trans. Am. Math. Soc. 356(2), 557–571 (2004)

    Article  MathSciNet  Google Scholar 

  14. Ru, M., Stoll, W.: The second main theorem for moving targets. J. Geom. Anal. 1(2), 99–138 (1991)

    Article  MathSciNet  Google Scholar 

  15. Thai, D.D., Quang, S.D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets. Internat. J. Math. 16(8), 903–939 (2005)

    Article  MathSciNet  Google Scholar 

  16. Thai, D.D., Quang, S.D.: Second main theorem with truncated counting function in several complex variables for moving targets. Forum Math. 20, 163–179 (2008)

    Article  MathSciNet  Google Scholar 

  17. 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. Roumanie 56(104)(4), 513–526 (2013)

    MathSciNet  MATH  Google Scholar 

  18. Tu, Z.-H.: Uniqueness problem of meromorphic mappings in several complex variables for moving targets. Tohoku Math. J. (2) 54(4), 567–579 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Funding

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

Author information

Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Si Duc Quang

  2. Thang Long Instutute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Si Duc Quang

  3. Faculty of Fundamental Sciences, Electric Power University, 235-Hoang Quoc Viet, Tu Liem, Ha Noi, Vietnam

    Ha Huong Giang

Authors
  1. Si Duc Quang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ha Huong Giang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Si Duc Quang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Quang, S.D., Giang, H.H. Algebraic Dependences of Three Meromorphic Mappings Sharing Few Moving Hyperplanes. Acta Math Vietnam 45, 739–748 (2020). https://doi.org/10.1007/s40306-019-00350-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40306-019-00350-5

Keywords

Mathematics Subject Classification (2010)

Search

Navigation