Zero distribution of some difference polynomials

Abstract

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) − afⁿ(z) and f(z)f(z + c₁) ⋯ 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.