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Uniqueness theorems on entire functions and their difference operators or shifts. (English) Zbl 1258.30010
Uniqueness theory of meromorphic functions is an important part of the Nevanlinna theory. The authors study the uniqueness problems on entire functions and their difference operators or shifts. The main result is a difference analogue of a result of {\it G. Jank} et al. [Complex Variables, Theory Appl. 6, 51--71 (1986; Zbl 0603.30037)], which is concerned with the uniqueness of the entire function sharing one finite value with its derivatives. Moreover, two relative results are proved, and examples are provided for their results.

30D35Distribution of values (one complex variable); Nevanlinna theory
30D10Representations of entire functions by series and integrals
Full Text: DOI
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[3] C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, vol. 557 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. · Zbl 1232.06020
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[11] J.-L. Zhang, “Value distribution and shared sets of differences of meromorphic functions,” Journal of Mathematical Analysis and Applications, vol. 367, no. 2, pp. 401-408, 2010. · Zbl 1188.30044 · doi:10.1016/j.jmaa.2010.01.038
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