一类差分多项式的零点和唯一性  

Zeros and uniqueness of a class of difference polynomials

作　　者：王乙萍 黄志刚[1] WANG Yiping;HUANG Zhigang(School of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou Jiangsu 215000,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215000

出　　处：《华东师范大学学报（自然科学版）》2021年第1期28-35,共8页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11971344);苏州科技大学研究生科研创新计划(SKCX18-Y03)。

摘　　要：主要运用Nevanlinna值分布理论研究了差分多项式的唯一性和零点分布,得到了关于差分多项式P(f)∑^(k)i=1^(t)if(z+c_(i)的唯一性结果和关于差分多项式P(f)∑^(k)i=1^(b)-(i)(z)f(z+c_(i)))^(s)-b_(0)(z)的零点分布结果,其中f (z)是有限级超越整函数,c_(i), t_(i) (i=1, 2,···, k)是非零复常数,b_(i)(z)(i=0, 1,···, k)是关于f(z)的小函数.In this paper, we investigate the uniqueness and distribution of zeros of a class of difference polynomials by using Nevanlinna’s value distribution theory. We obtain results about the uniqueness of the difference polynomials P(f)∑^(k)i=1^(t)if(z+c_(i) and the distribution of zeros of the difference polynomialsP(f)∑^(k)i=1^(b)-(i)(z)f(z+c_(i)))^(s)-b_(0)(z), where f(z) is a transcendental entire function of finite order,ci, t_(i)(i = 1, 2, · · ·, k) are non-zero constants, and b_(i)(z)(i = 0, 1, · · ·, k) are small functions with respect to f(z).

关 键 词：整函数 有限级 差分多项式 唯一性 零点 

分 类 号：O174.52[理学—数学]