涉及差分分担值的整函数唯一性

Uniqueness of the Entire Function Concerned with Difference Sharing Value

研究了Brücke猜想的差分模拟.利用Borel引理以及Nevanlinna值分布理论中关于周期函数的性质,将满足条件的整函数级大于等于1时可能出现的各类情况一一排除,再通过已证明的有限级整函数唯一性结论,得到了超级小于1且具有Picard例外函数的整函数及其差分CM分担0时这个整函数所具有的形式.此外,还利用了Nevanlinna值分布理论关于级的一些结论,从而使Borel引理可以在定理证明中反复应用,此方法适用于分担值以及某些差分分担周期函数的情况.

The difference counterpart of the Brücke conjecture was investigated.By virtue of the Borel lemma and the property about periodic functions in the Nevanlinna's value distribution theory to exclude all cases which may occurr when the order of an entire function satisfying some conditions is greater than or equal to 1,and utilizing some proved conclusions about the uniqueness of entire function of finite order,it is proved that if an entire function of hyper-order,which has a small Picard exceptional function,shares the value of 0 with its difference operator,then the form of this entire function can be obtained.In addition,some results about the order in Nevanlinna's value distribution theory have been also adopted,so that Borel lemma can be applied repeatedly in the theorem proving.The method is suited to the sharing value and some cases of difference sharing periodic functions.