Uniqueness Theorems on Difference Monomials of Entire Functions

Gang Wang, Deng-li Han and Zhi-Tao Wen

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: The aim of this paper is to discuss the uniqueness of the difference monomials fnf(z + c). It assumed that f and g are transcendental entire functions with finite order and Ek)(1, fnf(z + c)) = Ek)(1, gng(z + c)), where c is a nonzero complex constant and n, k are integers. It is proved that if one of the following holds (i) n ≥ 6 and k = 3, (ii) n ≥ 7 and k = 2, and (iii) n ≥ 10 and k = 1, then fg = t1 or f = t2g for some constants t2 and t3 which satisfy t2n+1=1 and t3n+1=1. It is an improvement of the result of Qi, Yang and Liu.

Date: 2012
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https://doi.org/10.1155/2012/407351

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:407351

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