整函数及其线性微分多项式的唯一性  

Uniqueness for Entire Function and Its Linear Differential Polynomial

作　　者：徐万松[1] 方明亮[1] 

机构地区：[1]南京航空航天大学理学院,南京师范大学数学系

出　　处：《南京航空航天大学学报》1995年第6期764-767,共4页Journal of Nanjing University of Aeronautics & Astronautics

摘　　要：１９７６年，ＬＲｕｂｅｌ与ＣＣＹａｎｇ对整函数及其导数分享两个复数（计重数）的唯一性作了研究。最近，顾永兴考虑将函数的导数换为函数的一般线性微分多项式，并证明了相应的唯一性定理。但定理中对两个复数以及多项式的系数（为函数的小函数）所作的一些限制是不自然的，他本人猜测，这些限制条件可以去掉。本文第二作者证实了他的猜测。本文则考虑整函数及其线性微分多项式在不计重数地分享两个有穷复数这一更一般的情况下的唯一性问题，得到了一个充分条件。In 1976 L Rubel and C C Yang studied the uniqueness for entire function and its derivative that share two values by counting multiplicity. Recently, Gu Y X replaced the derivative by a linear differential polynomial and proved the theorem. However, the restriction he added in the theorem on the values and coefficients of the polynomial is not necessary. He stated that it might be disregarded,the second author of the paper confirmed his statement. In this paper the authors consider a more general Case, that is, the entire function and its linear differential polynomial share two by values ignoring multiplicity, and obtain a sufficient condition for uniqueness.

关 键 词：复分析 唯一性 整函数 线性多项式 导数 

分 类 号：O174.52[理学—数学]