The 3-part of the ideal class group of a certain family of real cyclotomic fields
作者: Eleni Agathocleous
作者单位: 1University of Nicosia, Cyprus Ministry of Education, Cyprus
刊名: Acta Arithmetica, 2019, Vol.190 , pp.305-315
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/aa180716-7-10
原始语种摘要: We study the structure of the $3$-part of the ideal class group of a certain family of real cyclotomic fields with $3$-class number exactly $9$ and conductor equal to the product of two distinct odd primes. We employ known results from class field theory as well as theoretical and numerical results on real cyclic sextic fields, and we show that the $3$-part of the ideal class group of such cyclotomic fields must be cyclic. We present four examples of fields that fall into our category, namely the fields of conductor $3 \cdot 331$, $7 \cdot 67$, $3 \cdot 643$ and $7 \cdot 257$, and they are the only ones amongst all real cyclotomic fields with conductor $pq \leq 2021$. The $3$-part of the class number for the two fields of conductor $3 \cdot 643$ and $7 \cdot 257$ has been unknown up to...
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关键词翻译
关键词翻译
  • cyclotomic 割圆的
  • class 
  • ideal 理想
  • sextic 六次曲线
  • conductor 导线
  • certain 确实的
  • unknown 不知道的
  • group 
  • exactly 正确地
  • distinct 相异的