理想类群指数≤2的虚二次函数域

ON IMAGINARY QUADRATIC FUNCTION FIELDS WITH IDEAL CLASS GROUP OF EXPONENT < 2

本文给出虚二次函数域K=k^（1/2）D（k=Fq（x）,2+q）的理想类群指数≤2的一个必要条件.在某些条件下,这个条件也是充分的.特别地,给出了Louboutin[1]一个结果在函数域情形的模拟.

This paper presents a necessary condition for the ideal class group of an imaginary quadratic function field K = k(^(1/2)D) (k = Fq(x),2+q) to be of exponent ≤ 2. The condition is proved to be sufficient in some cases. Particularly, the authors present an analogue of S. Louboutin's result[1] in the case of function field.