成对型复微分差分多项式的零点与唯一性

Zeros and uniqueness of paired complex differential-difference polynomials

研究成对型复微分差分多项式P(f)L(g)-a(z)和P(g)L(f)-a(z)的零点情况,其中L(h)取线性微分多项式D(h),线性差分多项式Q(z,h)以及线性微分差分多项式D(z,h),P(z)是z的非常数多项式,a(z)是f(z)和g(z)的非零小函数。另外,研究了成对型复微分差分多项式分担公共小函数的唯一性问题。

In this paper,we study the zeros distribution of the paired differential-difference polynomials P(f)L(g)-a(z)and P(g)L(f)-a(z),where L(h)takes linear differential polynomials D(h)or linear difference polynomials Q(z,h)or linear differential-difference polynomials D(z,h),P(z)is a non-constant polynomial of z,and a(z)is a non-zero small function with respect to and f(z)and g(z).The related uniqueness problems of complex differential-difference polynomials are also considered.