JOURNAL ARTICLE
六次循环数域上的Ankeny-Artin-Chowla公式
Year: 1998 Journal: Chinese Science Bulletin (Chinese Version) Vol: 43 (5)Pages: 471-474 Publisher: Science China Press
Abstract
设K 6 为实六次循环数域 ,K 2 ,K 3 分别为其二次及三次子域 ,记h(L)为数域L的理想类数 .文中得到h- =h(K 6 ) /h(K 2 )h(K 3 )的 7个同余公式 .特别当K 6 的导子 f =p为素数 ,则Ch- ≡B ( p- 1) /6 B 5( p- 1) /6 (modp) ,其中C为明显给出的常数 ,B n 为Bernoulli数 ,这些结果相当系统地把Ankeny-Artin-Chowla ,Kiselev ,Carlitz,陆洪文 ,张贤科等从 1948到 1988年关于二次域及四次循环域的许多结果推广到实六次循环域上去 .
Keywords:
Mathematics
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Topics
Algebraic Geometry and Number Theory
Physical Sciences → Mathematics → Geometry and Topology
Meromorphic and Entire Functions
Physical Sciences → Mathematics → Applied Mathematics
Coding theory and cryptography
Physical Sciences → Computer Science → Artificial Intelligence
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