The simplest quartic fields with ideal class groups of exponents less than or equal to 2

• LOUBOUTIN Stéphane R.

  Institut de Mathématiques de Luminy

書誌事項

タイトル別名

• simplest quartic fields with ideal class groups of exponents less than or equal to 2

抄録

The simplest quartic fields are the real cyclic quartic number fields defined by the irreducible quartic polynomials x⁴-mx³-6x²+mx+1, where m runs over the positive rational integers such that the odd part of m²+16 is squarefree. We give an explicit lower bound for their class numbers which is much better than the previous known ones obtained by A. Lazarus. Then, using it, we determine the simplest quartic fields with ideal class groups of exponents ≤ 2.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 56 (3), 717-727, 2004

  一般社団法人 日本数学会

キーワード

• quartic field
• simplest quartic field
• class number
• class group
• zeta function

詳細情報

• CRID: 1390282680091869568
• NII論文ID: 10013358889
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1191334082
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2071669
• NDL書誌ID: 7015080
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7015080
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可