On value distribution of certain delay-differential polynomials

�m ABSTRACT: Given an entire function f of finite order & rho;, let L(z, f ) = j=0 bj(z)f (kj)(z+cj) be a linear delay-differential polynomial off with small coefficients in the sense of O(r & lambda;+) +S(r, f ), & lambda; < & rho;. Provided & alpha; and & beta; are similar small functions, we consider the zero distribution of L(z, f ) - & alpha;f n -& beta; for n > 3 and n = 2, respectively. Our results are improvements and complements of Chen [Abstract Appl Anal 2011 (2011):ID 239853), and Laine [J Math Anal Appl 469 (2019):808-826].

Automated summary

This paper improves and complements the research results of Chen and Laine, and investigates the zero distribution of a linear delay-differential polynomial with small coefficients.