CM-Fields with Cyclic Ideal Class Groups of 2-Power Orders
CM-Fields with Cyclic Ideal Class Groups of 2-Power Orders
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具有 2 次方循环理想类群的 CM 场
DOI：
10.1006/jnth.1997.2179
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发表时间：
1997
影响因子：
0.7
通讯作者：
S. Louboutin
中科院分区：
文献类型：
--
作者：
S. Louboutin
摘要证明了cm -域N中只有有限多个具有2次循环理想类群的cm -域N，其复共轭是N的某个自同构的平方，由于它们的实际确定太困难，我们仅满足于具有2次循环理想类群的2次非二次虚循环数域的确定。总共有22个这样的数字字段，其中10个属于第一类，9个属于第二类，3个属于第一类。本文的结论是对前人关于指数≥2的理想类群的所有2-幂次非二次虚环数域的结论的一个很好的补充。
Abstract We prove that there are only finitely many CM-fields N with cyclic ideal class groups of 2-power orders such that the complex conjugation is the square of some automorphism of N. Since their actual determination would be too difficult, we only content ourselves with the determination of the nonquadratic imaginary cyclic number fields of 2-power degrees with cyclic ideal class groups of 2-power orders. There are exactly 22 such number fields, 10 of them having class number one, 9 of them having class number two, and 3 of them having class number four. This present determination is a nice complement to the determination of all nonquadratic imaginary cyclic number fields of 2-power degrees with ideal class groups of exponents ⩽2 completed in an earlier paper.