[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.
[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.
Meromorphic functions sharing small functions with their difference polynomial in several variables
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.
[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.
[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.
Wang, M., & Liu, Z. (2023). Meromorphic functions sharing small functions with their difference polynomial in several variables. Hacettepe Journal of Mathematics and Statistics, 52(1), 73-90. https://doi.org/10.15672/hujms.1090815
AMA
Wang M, Liu Z. Meromorphic functions sharing small functions with their difference polynomial in several variables. Hacettepe Journal of Mathematics and Statistics. February 2023;52(1):73-90. doi:10.15672/hujms.1090815
Chicago
Wang, Minzhuo, and Zhixue Liu. “Meromorphic Functions Sharing Small Functions With Their Difference Polynomial in Several Variables”. Hacettepe Journal of Mathematics and Statistics 52, no. 1 (February 2023): 73-90. https://doi.org/10.15672/hujms.1090815.
EndNote
Wang M, Liu Z (February 1, 2023) Meromorphic functions sharing small functions with their difference polynomial in several variables. Hacettepe Journal of Mathematics and Statistics 52 1 73–90.
IEEE
M. Wang and Z. Liu, “Meromorphic functions sharing small functions with their difference polynomial in several variables”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, pp. 73–90, 2023, doi: 10.15672/hujms.1090815.
ISNAD
Wang, Minzhuo - Liu, Zhixue. “Meromorphic Functions Sharing Small Functions With Their Difference Polynomial in Several Variables”. Hacettepe Journal of Mathematics and Statistics 52/1 (February 2023), 73-90. https://doi.org/10.15672/hujms.1090815.
JAMA
Wang M, Liu Z. Meromorphic functions sharing small functions with their difference polynomial in several variables. Hacettepe Journal of Mathematics and Statistics. 2023;52:73–90.
MLA
Wang, Minzhuo and Zhixue Liu. “Meromorphic Functions Sharing Small Functions With Their Difference Polynomial in Several Variables”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, 2023, pp. 73-90, doi:10.15672/hujms.1090815.
Vancouver
Wang M, Liu Z. Meromorphic functions sharing small functions with their difference polynomial in several variables. Hacettepe Journal of Mathematics and Statistics. 2023;52(1):73-90.