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Ideal class groups of real quadratic fields of generalized ERD-type

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2 Author(s)
Xianke, Zhang ; Department of Applied Mathematics, Tsinghua University, Beijing 100084 ; Fuhua, Xu

Let $K = Q(bar{d})$ and d = s2 + r > 0. If r| 4s then K is the ERD-type. Here it is generalized to the types with r| 2ns, r| 4zns, or r| zns. Special properties of the class number h(d) and class group H(d) of K are proved. In particular, if d = a2t2 ± 2q+2t with prime q, then q| h(d) and H(d) contains a cyclic subgroup of order q provided 4 and 16 are not complete denominator of the simple continued-fraction of $bar{d}$. Both d = a2t2 ± 4zqt and d = a2t2/4 ± zqt have similar specialties.

Published in:

Tsinghua Science and Technology  (Volume:1 ,  Issue: 3 )