On value distribution of certain delay-differential polynomials

Abstract

Given an entire function f of finite order ρ, let L(z, f ) = m j=0 b j (z) f (k j ) (z+c j ) be a linear delay-differential polynomial of f with small coefficients in the sense of O(r λ+ ) + S(r, f ), λ < ρ. Provided α and β are similar small functions, we consider the zero distribution of L(z, f ) − α f n − β for n 3 and n = 2, respectively. Our results are improvements and complements of Chen