Abstract
In this paper, we discuss Picard values and the uniqueness problems for a differential polynomial of the form f n + a f (k).
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References
Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoamericana 11, 355–373 (1995)
Boussaf, K., Escassut, A., Ojeda, J.: p-adic meromorphic functions f ′ P ′(f),g ′ P ′(f) sharing a small function. Bull. Sci. Math. 136, 172–200 (2012)
Boutabaa, B., Escassut, A.: Urs and Ursim for p-adic meromorphic functions inside a disk. Proc. Edinburgh Math. Soc. 44, 485–504 (2001)
Chen, H.H., Fang, M.L.: On the value distribution of f n f ′. Sci. China Ser. A 38, 789–798 (1995)
Clunie, J.: On a result of Hayman. J. London Math. Soc. 42, 389–392 (1967)
Döringer, W.: Exceptional values of differential polynomials. Pacific J. Math. 98, 55–62 (1982)
Escassut, A.: Analytic Elements in p-dic Analysis. World Scientic Publishing (1995)
Escassut, A., Ojeda, J.: The p-adic Hayman conjecture when n = 2. Complex Variables 59(10), 1451–1455 (2014)
Fang, M.L., Hong, W.: A unicity theorem for entire functions concerning differential polynomials. Indian J. Pure Appl. Math. 32(9), 1343–1348 (2001)
Grahl, J., Nevo, S.: Differential polynomials and shared values. Ann. Acad. Sci. Fenn. Math. 36, 47–70 (2011)
Hayman, W.K.: Picard values of meromorphic functions and their derivatives. Ann. Math. 70(2), 9–42 (1959)
Hayman, W.K.: Research Problems in Function Theory. The Athlone Press University of London, London (1967)
Hu, P.C., Yang, C.C.: Meromorphic Functions over non-Archimedean Fields. Kluwer Academic Publishers (2000)
Khoai, H.H.: On p-adic meromorphic functions. Duke Math. J. 50, 695–711 (1983)
Khoai, H.H.: Height of p-adic holomorphic functions and applications. Int. Symp. Holomorphic Mappings, Diophantine Geometry and Related Topics, RIMS Lect. Notes Ser., Kyoto 819, 96–105 (1993)
Khoai, H.H., An, V.H.: Value distribution for p-adic hypersurfaces. Taiwan. J. Math. 7(1), 51–67 (2003)
Khoai, H.H., An, V.H., Lai, N.X: Value sharing problem and uniqueness for p-adic meromorphic functions. Annales Univ. Sci. Budapest., Sect. Comp. 38, 57–70 (2012)
Khoai, H.H., Quang, M.V.: On p-adic Nevanlinna theory. Lecture Notes Math. 1351, 146–158 (1988)
Lahiri, I., Dewan, S.: Value distribution of the product of a meromorphic function and its derivative. Kodai Math. J. 26, 95–100 (2003)
Lin, W., Yi, H.: Uniqueness theorems for meromorphic functions concerning fixed-points. Complex Variables 49(11), 793–806 (2004)
Mues, E.: Über ein problem von hayman. Math. Z. 164, 239–259 (1979)
Ojeda, J.: Hayman’s conjecture in a p-adic field. Taiwan. J. Math. 12(9), 2295–2313 (2008)
Ojeda, J.: Applications of the p-adic Nevanlinna theory to problems of uniqueness. Advances in p-adic and non-Archimedean analysis. Contemp. Math. 508, 161–179 (2010)
Ojeda, J.: Zeros of ultrametric meromorphic functions f ′ f n(f−a)k−α. Asian-European J. Math. 1(3), 415–429 (2008)
Ojeda, J.: Uniqueness for ultrametric analytic functions. Bull. Math. Soc. Sci. Math. Roumanie 54(102), 153–165 (2011)
Wang, Y.F.: On Mues conjecture and Picard values. Sci. China Ser. A 36, 28–35 (1993)
Yang, C.C., Hua, X.A.: Uniqueness and value-sharing of meromorphic functions. Ann. Acad. Sci. Fenn. Math. 22, 395–406 (1997)
Yi, H.X.: Meromorphic functions that share one or two values. Kodai Math. J. 22, 264–272 (1999)
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The authors would like to thank the referees for their valuable comments and suggestions to improve the quality of the paper.
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Tuan, P.D., Quang, N.T. Picard Values and Uniqueness for p-adic Meromorphic Functions. Acta Math Vietnam 41, 563–582 (2016). https://doi.org/10.1007/s40306-015-0166-4
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DOI: https://doi.org/10.1007/s40306-015-0166-4