Scholarlink

<p>We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic fields whose rings of integers have finite Pythagoras numbers, namely, one, two, three, and at least four.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pythagoras numbers for infinite algebraic fields

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月31日

查看全文
  • Nicolas Daans,
  • Stevan Gajović,
  • Siu Hang Man,
  • Pavlo Yatsyna

摘要

We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic fields whose rings of integers have finite Pythagoras numbers, namely, one, two, three, and at least four.