某些差分多项式的亏量

On Deficiencies of some Difference Polynomials

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果.

Halburd and Korhonen posed that the study of the value distribution ofcomplex differences plays an important role in the thrther study of complex differences and difference equations, which gained renewed interests recently. In this paper, we obtain some results on deficiencies of difference polynomials of meromorphic functions of finite order, some of which can be viewed as difference analogues of correspondingresults of differential polynomials. And under some conditions, a difference analogue of the classical Valiron-Mohon＇ko Theorem is also given as an important tool in this paper. These results improve previous findings.