Sums of three integral squares in biquadratic fields

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• 作者：Bin Zhang ^{zhangbin100902025@163.com" class="auth_mail} ; Chun-Gang Ji ; ^{cgji@njnu.edu.cn" class="auth_mail}
• 关键词：11E25 ; 11R16 ; 11R33
• 刊名：Journal of Number Theory
• 出版年：May, 2014
• 年：2014
• 卷：138
• 期：Complete
• 页码：37-47
• 全文大小：246 K

文摘

Text

Let K be an algebraic number field and the ring of integers in K. Let be the set of all elements which are sums of squares in and the minimal number of squares necessary to represent 鈭? in . Let be the smallest positive integer t such that every element in is a sum of t squares in . In this note, for , where are two distinct positive square-free integers, we show that and if , then .

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