论文标题
普通CM场，一级
Normal CM-fields with class number one
论文作者
论文摘要
我们表明，假设没有普通的Riemann假设，则没有正常的CM场，其中类别为64和96。这是通过使用Lee-Kwon的判别边界构造正常CM场的完整表来完成的。这解决了假设GRH的正常CM场的第一类问题。使用相同的技术在16、32、56和82中解决相对级别的第一问题，也可以解决相应的相对级别第一问题，假设GRH解决了。
We show that assuming the generalized Riemann hypothesis there are no normal CM-fields with class number one of degree 64 and 96. This is done by constructing complete tables of normal CM-fields using discriminant bounds of Lee--Kwon. This solves the class number one problem for normal CM-fields assuming GRH. Using the same technique to solve the relative class number one problem in degrees 16, 32, 56 and 82, also the corresponding relative class number one problem is solved assuming GRH.
