代数体函数微分单项式的值分布

On value distribution of differential monomial of algebroid functions

利用Nevanlinna代数体函数的值分布理论,讨论了代数体函数微分单项式的值分布问题,得到了:设w(z)是一个v值代数体函数,那么当n≥(l2+2σ+2l0+4)v-2σ-2时,(w')i1…(w(n))in(w(z))n取任意非零有限复数无穷多次,除非w(z)是代数函数.

Using Nevanlinna theory of value distribution of algebroid functions, the value distribution problem of algebroid differential monomial is discussed, we obtain this result： Let w（z） be a v value al- gebroid function, and n≥（l2＋2σ＋2l0＋4）v-2σ-2then（w＇）i1……（w（n））in（w（z）） assumes all values except possibly zero infinitely often, unless w（z） is algebraic.