Zero distribution of some difference polynomials

In this paper, suppose that a, c ∈ ℂ {0}, c j ∈ ℂ( j = 1, 2, ⋯, n ) are not all zeros and n ≥ 2, and f ( z ) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros, the zero distribution of difference polynomials of f ( z + c ) − a...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2023-09, Vol.38 (3), p.392-402
Main Authors: Li, Qian, Liu, Dan, Huang, Zhi-bo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Entire functions
Mathematics
Mathematics and Statistics
Polynomials
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Summary:In this paper, suppose that a, c ∈ ℂ {0}, c j ∈ ℂ( j = 1, 2, ⋯, n ) are not all zeros and n ≥ 2, and f ( z ) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros, the zero distribution of difference polynomials of f ( z + c ) − af n ( z ) and f ( z ) f ( z + c 1 ) ⋯ f ( z + c n ) are investigated. A number of examples are also presented to show that our results are best possible in a certain sense.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-023-4179-9