实二次域Q(P(1/2))(p≡3(mod 4))类数的上界

An Upper Bound for Class Numbers of Real Quadratic Fields Q(■) with p≡3(mod 4)

设p是适合p≡3（Pod4）的奇素数，h,ε分别是实二次域Q的类数和基本单位．本文运用初等方法证明了：εh＜（p+a+2)a+2/4(a+2)!。

Let p be an odd prime. Let h and ε denote the class number and thefundamental unit of the real qnadratic field Q( p) respectively In this paper, usingsome e1ementary methods, we prove that if p ≡ 3 (mod 4), then 6h εh< (p+α+2)α+2/4(α+2)！, where α = [( p + 1)/2l.