关于 P^k(P>3)元域 F的单超越扩域E上的三次方程的根的问题

The Threetimes Equation Root Problem Over a Simple Transcendental Extension Field E of a Field F of P^k(P>3) Elements

设 F是 Pk( P>3)元域 ,E是 F的单超越扩域 .本文给出 E上的三次方程 y3+Ay+B=0在 E中有根或没有根的条件 ,若方程有根 。

Let F be a field of P k(P>3) elements and E be a simple transcendental extension field of F. In this paper,we give the conditions that a threetimes equation y 3+Ay+B=0 over E has roots or has no roots in E .If the equation has roots,then we give the number of roots at the same time.