Uniqueness for the difference monomials of \(p\)-adic entire functions. (English) Zbl 1435.30134

Summary: The aim of this paper is to discuss the uniqueness of \(p\)-adic difference monomials \(f^nf(z+c)\). The results obtained in this paper are the \(p\)-adic analogues and supplements of the theorems given by X.-G. Qi et al. [Comput. Math. Appl. 60, No. 6, 1739–1746 (2010; Zbl 1202.30045)], G. Wang et al. [Abstr. Appl. Anal. 2012, Article ID 407351, 8 p. (2012; Zbl 1247.30047)], C.-C. Yang and X. Hua [Ann. Acad. Sci. Fenn., Math. 22, No. 2, 395–406 (1997; Zbl 0890.30019)].


30G06 Non-Archimedean function theory
30D20 Entire functions of one complex variable (general theory)
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI Euclid


[1] W.W. Adam and E.G. Straus, Non-Archimedean analytic functions taking the same values at the same points, Illinois. J. Math. 15(1971), 418-424. · Zbl 0215.13202
[2] V.H. An and H.H. Khoai, Value sharing problems for p-adic meromorphic functions and their difference polynomials, Ukranian Math. J. 64(2012), 147-164. · Zbl 1272.30066
[3] K. Boussaf, A. Escassut and J. Ojeda, New results on applications of Nevanlinna methods to value sharing problems, P-adic Numbers, Ultrametric Analysis and Applications, 5(2013), 278-301. · Zbl 1309.30038
[4] K. Boussaf, A. Escassut and J. Ojeda, P-adic meromorphic functions sharing a small function, Bull. Sci. Math. 136(2012), 172-200. · Zbl 1255.30047
[5] A. Boutabaa, Theorie de Nevanlinna p-adique, Manuscript Math. 67(1990), 251-269. · Zbl 0697.30047
[6] A. Boutabaa, A. Escassut and L. Haddad, On uniqueness of p-adic entire functions, Indag. Math. 8(1997), 145-155. · Zbl 0935.30029
[7] A. Boutabaa and A. Escassut, URS and URSIMS for p-adic meromorphic functions inside a disk, Proc. Edinburgh Math. Soc. 44(2001), 485-504. · Zbl 1002.12008
[8] W. Cherry and C.C. Yang, Uniqueness of non-archimedean entire functions sharing sets of values counting multiplicities, Proc. Amer. Math. Soc. 127(1998), 967-971. · Zbl 0993.30026
[9] J. Clunie, On a result of Hayman, J. Lond. Math. Soc. 42(1967), 389-392. · Zbl 0169.40801
[10] W.K. Hayman, Reserch problems in function theory, University of London, The Athlone Press, London, 1967.
[11] W.K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. Math. 70(1959), 9-42. · Zbl 0088.28505
[12] P.C. Hu, and C.C. Yang, Meromorphic functions over non-archimedean fields, Kluwer, Dordrecht, 2000. · Zbl 0984.30027
[13] H.H. Khoai, On p-adic meromorphic functions, Duke Math. J. 50(1983), 695-711. · Zbl 0544.30039
[14] H.H. Khoai and, Value distribution for p-adic hypersurfaces, Taiwanese J. Math. 7(2003), 51-67. · Zbl 1090.32008
[15] H.H. Khoai and M.V. Quang, On p-adic Nevanlinna theory, Lecture Notes in Mathematics, Vol. 1351, Springer-Verlag, Berlin, 1988, 146-158. · Zbl 0673.30035
[16] H.H. Khoai, Vu Hoai An and N.X. Lai, Value sharing problem and uniqueness for p-adic meromorphic functions, Annales Univ. Sci. Budapest. Sect. Comp.38(2012), 57-70. · Zbl 1274.30158
[17] J. Ojeda, On Hayman’s conjecture over a p-adic field, Taiwanese J. Math. 12(2008), 2295-2313. · Zbl 1189.30088
[18] J. Ojeda, Applications of the p-adic Nevanlinna theory to problems of uniqueness, Advances in p-adic and non-Archimedean Analysis, Contemporary Mathematics, 508(2010), 161-179. · Zbl 1288.30047
[19] J. Ojeda, Uniqueness for ultrametric analytic functions, Bull. Math. Soc. Sci. Math. Roumanie. 54(2011), 153-165. · Zbl 1240.30205
[20] P.D. Tuan and N.T. Quang, Picad values and uniqueness for p-adic meromorphic functions, Acta Math Vietnam. 41(2016), 563-582. · Zbl 1369.30048
[21] X.G. Qi, L.Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl. 60(2010), 1739-1746. · Zbl 1202.30045
[22] G. Wang, D.L. Han and Z.T. Wen, Uniqueness theorems on difference monomials of entire functions, Abstract Appl. Anal. 2012(2012), Article ID 407351. · Zbl 1247.30047
[23] J.T.Y. Wang, Uniqueness polynomials and bi-unique range sets, Acta Arith. 104(2002), 183-200. · Zbl 1011.30043
[24] C.C. Yang and X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22(1997), 395-406. · Zbl 0890.30019
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