关于微分-差分多项式的零点和唯一性

On zeros and uniqueness of differential-difference polynomials

利用Nevanlinna值分布理论,研究零级超越整函数的微分-差分多项式[f(qz+c)n∏mj=1 f(j)(z)](k)关于小函数α(z)的零点分布,其中n、j、m、k都是正整数且n≥m(m+5)/2+k+2;此外,得到了2个零级超越整函数的微分-差分多项式[f(qz+c)n∏m j=1 f(j)(z)](k)与[g(qz+c)n∏m j=1 g(j)(z)](k)CM分担一个值的唯一性结果,其中n、j、m、k都是正整数且n≥m(m+7)/2+2k+5.

By Nevanlinna value distribution theory,this paper investigates the zeros distribution of a differential-difference polynomial of a transcendental entire function with zero order [f(qz+c)n∏mj=1 f(j)(z)](k) concerning a small function α(z),where n j,m,k are positive integers and n≥m(m+5)/2+k+2.Furthermore,the uniqueness result of a differential-difference polynomial [f(qz+c)n∏m j=1 f(j)(z)](k) sharing one value with the other differential-difference polynomial [g(qz+c)n∏m j=1 g(j)(z)](k) is obtained,where n,j,m,k are positive integers and n≥m(m+7)/2+2k+5.