关于一类实二次域的类数与基本单位的上界

Upper Bounds of the Class Number and the Fundamental Unit of Real Quadratic Field Q((p(1/2))

设素数P≡1(mod4),k,ε分别表示实二次域Q(p^(1/2))类数和基本单位．本文改进了类数h和基本单位ε的上界,证明了:hlogeε<1/4(p^(1/2)+6)log(2ep^(1/2)),并得到了几个重要的推论．

Let p be an odd prime. Let h and ε denote the class number and the fundamental unit of the real quadratic field Q（√p）, respectively. This paper proves that if p =1（mod4）, then hlog ε 〈 1/4（√p ＋ 6）log（2e√p）.