Arithmetic of quasi-cyclotomic fields

作者：Yin Linsheng^*; Zhang Chong

来源：Journal of Number Theory, 2008, 128(6): 1717-1730.

DOI：10.1016/j.jnt.2007.04.014

We call a quadratic extension of a cyclotomic field a quasi-cyclotomic field if it is non-abelian Galois over the rational number field. In this paper, we study the arithmetic of any quasi-cyclotomic field, including to determine the ring of integers of it, the decomposition nature of prime numbers in it, and the structure of the Galois group of it over the rational number field. We also describe explicitly all real quasi-cyclotomic fields, namely, the maximal real subfields of quasi-cyclotomic fields which are Galois over the rational number field. It gives a series of totally real fields and CM fields which are non-abelian Galois over the rational number field.

• 出版日期2008-6
• 单位清华大学