实二次函数域基本单位的范

ON THE NORMS OF FUNDAMENTAL UNITS IN REAL QUADRATIC FUNCTION FIELDS

作为Ｈ．Ｆ．Ｔｒｏｔｅｒ［３］中一个结果的模拟，本文给出实二次函数域Ｋ中基本单位ε的范为Ｎ（ε）＝ｇ的一些充分必要条件，其中ｇ为Ｋ的常数域Ｆｑ的非零乘法群Ｆ＊ｑ的生成元（２ｑ）。利用图论的语言，本文还给出了Ｎ（ε）＝ｇ的一些充分条件，这些条件对于数域也同样地适用。

As a analogue to a resuit of H.F. Trotter , this paper presents some sufficient and necessary conditions When N(ε)=g. where ε is the fundamental unit of a real quadratic function field with constant field F q (2q) and g is a generator of F * q. By the language of Graph Theory, we also establish some sufficient conditions about N(ε)=g, which are true for real quadratic number fields. Our work generalize that of Trotter and the others.