We discuss the value-sharing problem, versions of the Hayman conjecture, and the uniqueness problem for *p*-adic meromorphic functions, as well as their difference operators and difference polynomials.

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## References

W. W. Adam and E. G. Straus, “Non-Archimedean analytic functions taking the same values at the same points,”

*Ill. J. Math.*,**15**, 418–424 (1971).A. Alotaibi, “On the Zeros of

*af*(*f*^{(k)})^{n}for*n*≥ 2;”*Comput. Methods Funct. Theory*,**4**, No. 1, 227–235 (2004).A. Boutabaa and A. Escassut, “Uniqueness problems and applications of the ultrametric Nevanlinna theory,”

*Contemp. Math.*,**319**, 53–74 (2003).H. H. Chen and M. L. Fang, “On the value distribution of

*f*^{n}*f*′;”*Sci. China Ser. A*,**38**, 789–798 (1995).J. Clunie, “On a result of Hayman,”

*J. London Math. Soc.*,**42**, 389–392 (1967).A. Escassut, J. Ojeda, and C. C. Yang, “Functional equations in a

*p*-adic context,”*J. Math. Anal. Appl.*,**351**, No. 1, 350–359 (2009).F. Gross and C. C. Yang, “On preimages and range sets of meromorphic functions,”

*Proc. Jpn. Acad.*,**58**, 17–20 (1982).Ha Huy Khoai, “On p-adic meromorphic functions,”

*Duke Math. J.*,**50**, 695–711 (1983).Ha Huy Khoai, “Height of p-adic holomorphic functions and applications,”

*Internat. Symp. “Holomorphic Mappings, Diophantine Geometry, and Related Topics” (Kyoto, 1992). Surikaisekikenkyusho Kokyuroku*, No. 819, 96–105 (1993).Ha Huy Khoai and Mai Van Tu, “

*p*-Adic Nevanlinna–Cartan theorem,”*Int. J. Math.*,**6**, 719–731 (1995).Ha Huy Khoai and Vu Hoai An, “Value distribution for

*p*-adic hypersurfaces,”*Taiwan. J. Math.*,**7**, No. 1, 51–67 (2003).Ha Huy Khoai and Vu Hoai An, “Value distribution problem for

*p*-adic meromorphic functions and their derivatives,”*Ann Toulouse*(to appear).Ha Huy Khoai and My Vinh Quang, “On

*p*-adic Nevanlinna theory,”*Lect. Notes Math.*,**1351**, 146–158 (1988).R. G. Halburd and R. J. Korhonen, “Nevanlinna theory for the difference operator,”

*Ann. Acad. Sci. Fenn. Math.*,**31**, 463–478 (2006).Q. Han and P.-C. Hu, “Unicity of meromorphic functions related to their derivatives,”

*Bull. Belg. Math. Soc. Simon Stevin*,**14**, 905–918 (2007).W. K. Hayman,

*Research Problems in Function Theory*, London Athlone Press Univ., London (1967).P.-C. Hu and C.-C. Yang,

*Meromorphic Functions over Non-Archimedean Fields*, Kluwer, Dordrecht (2000).K. Liu and L. Z. Yang, “Value distribution of the difference operator,”

*Arch. Math.*,**92**, No. 3, 270–278 (2009).I. Lahiri and S. Dewan, “Value distribution of the product of a meromorphic function and its derivative,”

*Kodai Math. J.*,**26**, 95–100 (2003).I. Lahiri and C.-C. Yang, “Value distribution of difference polynomials,”

*Proc. Jpn. Acad., Ser. A*,**83**, No. 8, 148–151 (2007).S. Nevo, X. C. Pang, and L. Zalcman, “Picard–Hayman behavior of derivatives of meromorphic functions with multiple zeros,”

*Electron. Res. Announc. Amer. Math. Soc.*,**12**, 37–43 (2006).J. Ojeda, “Hayman’s conjecture in a

*p*-adic field,”*Taiwan. J. Math.*,**12**, No. 9, 2295–2313 (2008).C.-C. Yang and X. H. Hua, “Uniqueness and value-sharing of meromorphic functions,”

*Ann. Acad. Sci. Fenn. Math.*,**22**, 395–406 (1997).

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 2, pp. 147–164, February, 2012.

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An, V.H., Khoai, H.H. Value-sharing problem for *p*-adic meromorphic functions and their difference operators and difference polynomials.
*Ukr Math J* **64**, 163–185 (2012). https://doi.org/10.1007/s11253-012-0636-y

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DOI: https://doi.org/10.1007/s11253-012-0636-y

### Keywords

- Entire Function
- Meromorphic Function
- Difference Operator
- Uniqueness Problem
- Transcendental Entire Function