Abstract
In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f nm(z)f nd(qz + c))(k) for meromorphic functions in a non-Archimedean field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.-P. Bezivin, K. Boussaf and A. Escassut, “Zeros of the derivative of a p-adic meromorphic function,” Bull. Sci. Mathematiques 136 (8), 839–847 (2012).
A. Boutabaa, “Théorie de Nevanlinna p-adique,”ManuscriptaMath. 67, 251–269 (1990),.
K. Boussaf, A. Escassut and J. Ojeda, “p-adic meromorphic functions (f)(')P'(f), (g)(')P'(g) sharing a small function,” Bull. Sci. math. 136, 172–200 (2012).
A. Escassut and J. Ojeda, “The p-adicHayman conjecturewhenn=2,” ComplexVar. Ell. Equ. 59 (10), 1451–1456 (2014).
A. Escassut, Value Distribution in p-Adic Analysis (World Sci. Publ. Co. Pte. Ltd. Singapore, 2015).
C. Y. Fang and M. L. Fang, “Uniqueness of meromorphic functions and differential polynomials,” Comput. Math. Appl., 44, 607–617 (2002).
Ha Huy Khoai, “On p-adic meromorphic functions,” Duke Math. J. 50, 695–711 (1983).
Ha Huy Khoai and Vu Hoai An, “Value distribution for p-adic hypersurfaces,” Taiwanese J. Math. 7 (1), 51–67 (2003).
Ha Huy Khoai and Vu Hoai An, “Value distribution problem for p-adic meromorphic functions and their derivatives,” Ann. Fac. Sc. Toulouse, Vol. XX, No. Special, 135–149 (2011).
Ha Huy Khoai and Vu Hoai An, “Value sharing problem for p-adicmeromorphic functions and their difference operators and difference polynomials,” Ukranian Math. J. 64 (2), 147–164 (2012).
Ha Huy Khoai, Vu Hoai An and Nguyen Xuan Lai, “Value sharing problem and uniqueness for p-adic meromorphic functions,” Ann. Univ. Sci. Budapest., Sect. Comp. 38, 71–92 (2012).
W. K. Hayman, Meromorphic Functions (Clarendon Press, Oxford, 1964).
P. C. Hu and C. C. Yang, Meromorphic Functions over Non-Archimedean Fields (Kluwer Acad. Publishers, 2000).
I. Laine and C. C. Yang, “Value distribution of difference polynomials,” Proc. Japan. Acad. Ser. A 83 (8), 148–151 (2007).
I. Lahiri, “Uniqueness of meromorphic functions as governed by their differential polynomials,” Yokohama Math. J. 44, 147–156 (1997).
K. Liu, X. Liu and T. B. Cao, “Value distribution and uniqueness of difference polynomials,” Adv. Difference Equ., article ID 234215, 12 pp. (2011).
J. Ojeda, “Hayman’s conjecture in a p-adic field,” Taiwanese J. Math. 12 (9), 2295–2313 (2008).
X. C. Qi, L. Z. Yang and K. Liu, “Uniqueness and periodicity of meromorphic functions concerning the difference operator,” Comp.Math. Appl. 60 (6), 1739–1746 (2010).
M. Ru, “A note on p-adic Nevanlinna theory,” Proc. Amer. Math. Soc. 129, 1263–1269 (2001).
C. C. Yang, “On two entire functions, which together with their first derivatives have the same zeros,” J. Math. Anal. Appl. 56, 1–6 (1976).
H. X. Yi. “A question of C. C. Yang on the uniqueness of entire functions,” KodaiMath. J. 13, 39–46 (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
An, V.H., Hoa, P.N. & Khoai, H.H. Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field. P-Adic Num Ultrametr Anal Appl 9, 1–14 (2017). https://doi.org/10.1134/S2070046617010010
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070046617010010