相对二次扩张的分歧性与实二次域的基本单位（英文）

Ramification in relative quadratic extensions and fundamental units of real quadratic fields

设F=Q(d)为实二次域,ε=x+yd为F的基本单位,并且ε满足NF/Q(ε)=1.建立起二次扩张F(ε)/F的二进素理想的分歧性质和x,y的同余性质之间的联系.并在d=p1…pr或2p1…pr的情形下,给出x,y的一些同余性质,其中,p1,…,pr为模4余1的不同素数.

Let F=QQ(d)be areal quadratic field andε=x+yd the fundamental unit of F satisfying NF/Q(ε)=1.Some connections between the ramification properties for dyadic prime ideals in quadratic extension F(ε)/Fand congruence properties of x,y were established.As a corollary,some congruence properties about x,y were given when d=p1…pror 2p1…pr with p1≡…≡pr≡1mod 4being distinct prime numbers.