Skip to main content
Log in

Results on Certain Difference Polynomials and Shared Values

  • Published:
Computational Methods and Function Theory Aims and scope Submit manuscript

Abstract

In this paper, we study uniqueness questions for meromorphic functions for which certain difference polynomials share a finite non-zero value, and give mathematical expressions for the meromorphic functions in the conclusions of the main results in the present paper, which are the related to the questions studied in Li–Yu (Bull Korean Math Soc 55(5):1529–1561, 2018).

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Brosch, G.: Eindeutigkeitssätze für meromorphe Funktionen, Thesis. Technical University of Aachen, Aachen (1989)

    MATH  Google Scholar 

  2. Chen, Z.X.: Complex Differences and Difference Equations. Science Press, Beijing (2014)

    Book  Google Scholar 

  3. Chiang, Y.M., Feng, S.J.: On the Nevanlinna characteristic of \(f(z+\eta )\) and difference equations in the complex plane. Ramanujan J. 16(1), 105–129 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Grahl, J., Nevo, S.: Differential polynomials and shared values. Ann. Acad. Sci. Fenn. Math. 36(1), 47–70 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gundersen, G.G.: Meromorphic functions that share three or four values. J. Lond. Math. Soc. 20(3), 457–466 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gundersen, G.G., Tohge, K.: Unique range sets for polynomials or rational functions, Progress in Analysis, pp. 235–246 (2003)

  7. Halburd, R.G., Korhonen, R.J.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314(2), 477–487 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Halburd, R.G., Korhonen, R.J.: Nevanlinna theory for the difference operator. Ann. Acad. Sci. Fenn. Math. 31(2), 463–478 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Halburd, R.G., Tohge, K.: Holomorphic curves with shift-invariant hyperplane preimages. Trans. Am. Math. Soc. 366(8), 4267–4298 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hayman, W.K.: Meromorphic Functions. Clarendon Press, Oxford (1964)

    MATH  Google Scholar 

  11. Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Zhang, J.L.: Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity. J. Math. Anal. Appl. 355(1), 352–363 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J.: Uniqueness of meromorphic functions sharing values with their shifts. Complex Var. Ellipt. Equ. 56(1–4), 81–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lahiri, I.: Weighted sharing of three values and uniqueness of meromorphic functions. Kodai Math. J. 24(3), 421–435 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Laine, I.: Nevanlinna Theory and Complex Differential Equations. Walter de Gruyter, Berlin (1993)

    Book  MATH  Google Scholar 

  15. Li, P., Yang, C.C.: On the characteristics of meromorphic functions that share three values CM. J. Math. Anal. Appl. 220(1), 132–145 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, X.M., Yu, H.: Certain difference polynomials and shared values. Bull. Korean Math. Soc. 55(5), 1529–1561 (2018)

    MathSciNet  MATH  Google Scholar 

  17. Mokhonko, A.Z.: On the Nevanlinna characteristics of some meromorphic functions. In: Theory of Functions, Functional Analysis and Their Applications, vol. 14, Izd-vo Khar’kovsk. Un-ta, pp. 83–87 (1971)

  18. Yang, C.C., Yi, H.X.: Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, Dordrecht (2003)

    Book  MATH  Google Scholar 

  19. Yang, L.: Value Distribution Theory. Springer, Berlin (1993)

    MATH  Google Scholar 

  20. Yi, H.X.: Unicity theorems for meromorphic functions that share three values. Kodai Math. J. 18(2), 300–314 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, J.L.: Value distribution and shared sets of differences of meromorphic functions. J. Math. Anal. Appl. 367(2), 401–408 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang, Q.C.: Meromorphic functions sharing three values. Indian J. Pure Appl. Math. 30(7), 667–682 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors wish to express their thanks to the referee for his/her valuable suggestions and comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiao-Min Li.

Additional information

Communicated by Risto Korhonen.

Publisher's Note

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

Project supported in part by the NSFC (No. 11171184), the NSF of Shandong Province, China (No. ZR2019MA029), the FRFCU (No. 3016000841964007) and the Scientific Research Project of Shanxi Datong University (No. 2020K19).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, HC., Li, XM., Yu, H. et al. Results on Certain Difference Polynomials and Shared Values. Comput. Methods Funct. Theory 22, 663–682 (2022). https://doi.org/10.1007/s40315-022-00435-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40315-022-00435-7

Keywords

Mathematics Subject Classification

Navigation