A Generalization of Bruck's Conjecture for a Class of Entire Functions

作者：Lu, Feng^*; Yi, Hongxun

来源：Results in Mathematics, 2015, 68(1-2): 157-169.

DOI：10.1007/s00025-014-0428-9

• Differential equation
• Nevanlinna theory
• uniqueness
• normal family

In this paper, we study the uniqueness problem of entire functions sharing polynomials IM with their first derivative. As an application, we generalize Bruck's conjecture from sharing value CM to sharing polynomial IM for a class of functions. In fact, we prove a result as follows: Let a(not equivalent to 0) be a polynomial and n >= 2 be an integer, let f be a transcendental entire function, and let F = f(n). If F and F' share a IM, then f(z) = Ae(z/n), where A is a nonzero constant. It extends some previous related theorems.

• 出版日期2015-9
• 单位山东大学; 中国石油大学（北京）