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VALUE SHARING AND UNIQUENESS OF CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS

  • Samar Halder (Department of Mathematics JIS College of Engineering) ;
  • Pulak Sahoo (Department of Mathematics University of Kalyani)
  • Received : 2023.03.22
  • Accepted : 2024.10.02
  • Published : 2025.01.31

Abstract

We study the uniqueness problem of two different classes of meromorphic functions sharing two distinct values. Our results extend and complement the result of Li [12], and at the same time extend results due to Hao and Chen [7], and Wu and Hu [16]. Another result in this paper, besides finding a possible answer to a question raised in [1], extends and complements a recent result of Banerjee and Kundu [1] and that of Han [6].

Keywords

Acknowledgement

The authors are thankful to the referee for his/her valuable comments and useful suggestions towards the improvement of the paper.

References

  1. A. Banerjee and A. Kundu, A note on uniqueness of meromorphic functions sharing two singleton sets related to a question of Chen, Novi Sad J. Math. 52 (2022), 41–68. https://doi.org/10.30755/NSJOM.11151
  2. C. A. Berenstein and R. Gay, Complex Variables, Graduate Texts in Mathematics, 125, Springer, New York, 1991. https://doi.org/10.1007/978-1-4612-3024-3
  3. J.-F. Chen, Uniqueness of meromorphic functions sharing two finite sets, Open Math. 15 (2017), no. 1, 1244-1250. https://doi.org/10.1515/math-2017-0102
  4. J.-F. Chen, Meromorphic functions sharing unique range sets with one or two elements, Georgian Math. J. 28 (2021), no. 3, 349-354. https://doi.org/10.1515/gmj-2019-2073
  5. W. Doeringer, Exceptional values of differential polynomials, Pacific J. Math. 98 (1982), no. 1, 55–62. http://projecteuclid.org/euclid.pjm/1102734384 102734384
  6. Q. Han, Some uniqueness results related to L-functions, Boll. Unione Mat. Ital. 10 (2017), no. 4, 503–515. https://doi.org/10.1007/s40574-016-0081-1
  7. W.-J. Hao and J.-F. Chen, Uniqueness theorems for L-functions in the extended Selberg class, Open Math. 16 (2018), no. 1, 1291–1299. https://doi.org/10.1515/math-2018-0107
  8. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
  9. P.-C. Hu and B. Q. Li, A simple proof and strengthening of a uniqueness theorem for L-functions, Canad. Math. Bull. 59 (2016), no. 1, 119–122. https://doi.org/10.4153/CMB-2015-045-1
  10. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. https://doi.org/10.1017/S0027763000027215
  11. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), no. 3, 241–253. https://doi.org/10.1080/17476930108815411
  12. B. Q. Li, A result on value distribution of L-functions, Proc. Amer. Math. Soc. 138 (2010), no. 6, 2071–2077. https://doi.org/10.1090/S0002-9939-09-10222-8
  13. B. Q. Li, A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation, Adv. Math. 226 (2011), no. 5, 4198–4211. https://doi.org/10.1016/j.aim.2010.12.001
  14. A. Selberg, Old and new conjectures and results about a class of Dirichlet series, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), 367–385, Univ. Salerno, Salerno, 1992.
  15. J. Steuding, Value-Distribution of L-Functions, Lecture Notes in Mathematics, 1877, Springer, Berlin, 2007.
  16. A.-D. Wu and P.-C. Hu, Uniqueness theorems for Dirichlet series, Bull. Aust. Math. Soc. 91 (2015), no. 3, 389–399. https://doi.org/10.1017/S0004972714001166
  17. L. Yang, Value Distribution Theory, translated and revised from the 1982 Chinese original, Springer, Berlin, 1993.
  18. C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Acad. Publ., Dordrecht, 2003.