Year 2023,
, 73 - 90, 15.02.2023
Minzhuo Wang
,
Zhixue Liu
References
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differences, Results Math. 63 (1), 557-565, 2013.
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functions sharing values with their nth order exact differences, Anal. Math. 45 (2),
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2011.
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York, 2013.
- [13] R. Korhonen, A difference picard theorem for meromorphic functions of several variables,
Comput. methods funct. theory, 12v(1), 343-361, 2012.
- [14] I. Laine, Nevanlinna theory and complex differential equations, Berlin, Walter de
Gruyter, 1993.
- [15] P. Li, Unicity of meromorphic functions and their derivatives, J. math. anal. appl.
285 (2), 651-665, 2003.
- [16] Y.H. Li and J.Y. Qiao, The uniqueness of meromorphic functions concerning small
functions, Sci. China ser. A-math., 43 (6), 581-590, 2000.
- [17] Z.X. Liu and Q.C. Zhang, Difference uniqueness theorems on meromorphic functions
in several variables, Turkish J. Math. 42 (5), 2481-2505, 2018.
- [18] F. Lü and W. Lü, Meromorphic functions sharing three values with their difference
operators, Comput. methods funct. theory, 17 (3), 395-403, 2017.
- [19] E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung zwei
Werte teilen, Results Math. 6 (1), 48-55, 1983.
- [20] R. Nevanlinna, Einige Eindeutigkeitss¨atze in der Theorie der meromorphen Funktionen,
Acta Math. 48 (3), 367-391, 1926.
- [21] M. Ru, Nevanlinna theory and its relation to diophantine approximation, World Scientific
Publishing Co., Singapore, 2001.
- [22] L.A. Rubel and C.C. Yang, Values shared by an entire function and its derivative,
Complex anal. synerg. 599, 101-103, 1976.
- [23] P. Russmann, Uber Differentialpolynome, die mit ibres erzeugenden Funktion zwei
werte teilen, Dissertation, Technischen Universitit Berlin, 1993.
- [24] B.V. Shabat, Distribution of values of holomorphic mappings, Translations of Mathematical
Monographs, Amer. math. soc. 1985.
- [25] W.N. Wu and T.B. Cao, Uniqueness theorems of meromorphic functions and their
differences in several complex variables, Comput. methods funct. theory, 22v(2), 379-
399, 2021.
- [26] C.C. Yang and H.X. Yi, Uniqueness theory of meromorphic functions, Dordrecht, the
Netherlands: Kluwer Academic, 2003.
Meromorphic functions sharing small functions with their difference polynomial in several variables
Year 2023,
, 73 - 90, 15.02.2023
Minzhuo Wang
,
Zhixue Liu
Abstract
The aim of this paper is to deal with the uniqueness problem on meromorphic functions in $ \mathbb{C}^{m} $ sharing small functions with their difference polynomial, and the results obtained can be seen as some extensions of previous results from one complex variable to several complex variables.
References
- [1] C. Berenstein, D.C. Chang and B.Q. Li, A note on wronskians and linear dependence
of entire functions, Complex var. elliptic equ. 24 (1-2), 131-144, 1994.
- [2] Z.X. Chen, Complex differences and difference equations, Science press, Beijing, 2013.
- [3] Z.X. Chen and H.X. Yi, On sharing values of meromorphic functions and their
differences, Results Math. 63 (1), 557-565, 2013.
- [4] Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of $f(z+\eta)$ and difference
equations in the complex plane, Ramanujan J. 16 (1), 105-129, 2008.
- [5] N. Cui and Z.X. Chen, The conjecture on unity of meromorphic functions concerning
their differences, J. difference equ. appl. 22 (10), 1452-1471, 2016.
- [6] H. Fujimoto, On meromorphic maps into the complex projective space, J. math. soc.
Japan, 26 (2), 272-288, 1974.
- [7] Z.S. Gao, R. Korhonen, J.L. Zhang and Y.Y. Zhang, Uniqueness of meromorphic
functions sharing values with their nth order exact differences, Anal. Math. 45 (2),
321-334, 2019.
- [8] G.G. Gundersen, Meromorphic functions that share two finite values with their derivative,
Pacific J. Math. 105 (2), 299-309, 1983.
- [9] R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic
derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2),
477-487, 2006.
- [10] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann.
acad. sci. fenn. Math. 31, 463-478, 2006.
- [11] J. Heittokangas, R. Korhonen, I. Laine and J. Rieppo, Uniqueness of meromorphic
functions sharing values with their shifts, Complex var. elliptic equ. 56 (1-4), 81-92,
2011.
- [12] P.C. Hu, P. Li and C.C. Yang, Unicity of meromorphic mappings, Springer, New
York, 2013.
- [13] R. Korhonen, A difference picard theorem for meromorphic functions of several variables,
Comput. methods funct. theory, 12v(1), 343-361, 2012.
- [14] I. Laine, Nevanlinna theory and complex differential equations, Berlin, Walter de
Gruyter, 1993.
- [15] P. Li, Unicity of meromorphic functions and their derivatives, J. math. anal. appl.
285 (2), 651-665, 2003.
- [16] Y.H. Li and J.Y. Qiao, The uniqueness of meromorphic functions concerning small
functions, Sci. China ser. A-math., 43 (6), 581-590, 2000.
- [17] Z.X. Liu and Q.C. Zhang, Difference uniqueness theorems on meromorphic functions
in several variables, Turkish J. Math. 42 (5), 2481-2505, 2018.
- [18] F. Lü and W. Lü, Meromorphic functions sharing three values with their difference
operators, Comput. methods funct. theory, 17 (3), 395-403, 2017.
- [19] E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung zwei
Werte teilen, Results Math. 6 (1), 48-55, 1983.
- [20] R. Nevanlinna, Einige Eindeutigkeitss¨atze in der Theorie der meromorphen Funktionen,
Acta Math. 48 (3), 367-391, 1926.
- [21] M. Ru, Nevanlinna theory and its relation to diophantine approximation, World Scientific
Publishing Co., Singapore, 2001.
- [22] L.A. Rubel and C.C. Yang, Values shared by an entire function and its derivative,
Complex anal. synerg. 599, 101-103, 1976.
- [23] P. Russmann, Uber Differentialpolynome, die mit ibres erzeugenden Funktion zwei
werte teilen, Dissertation, Technischen Universitit Berlin, 1993.
- [24] B.V. Shabat, Distribution of values of holomorphic mappings, Translations of Mathematical
Monographs, Amer. math. soc. 1985.
- [25] W.N. Wu and T.B. Cao, Uniqueness theorems of meromorphic functions and their
differences in several complex variables, Comput. methods funct. theory, 22v(2), 379-
399, 2021.
- [26] C.C. Yang and H.X. Yi, Uniqueness theory of meromorphic functions, Dordrecht, the
Netherlands: Kluwer Academic, 2003.