正特征函数域上两类形式幂级数的超越性

TRANSCENDENCE OF TWO TYPES OF FORMAL POWER SERIES OVER FUNCTION FIELD WITH POSITIVE CHARACTERISTIC

本文研究了J.-Y.Yao引入的两类形式幂级数.J.-Y.Yao利用其建立的超越性判别准则,得到了它们在函数域上超越的充分必要条件,而本文将利用一种更为简单直接的方法来证明上述结论.

In this paper, we consider two types of formal power series introduced by J. -Y. Yao, who obtained, by using a transcendental criterion established by himself, a sufficient and necessary condition such that the two series in question are transcendental. In this work we shall use a simpler and more direct method to give a new proof of the above results.