论文标题
在某些复杂双重季度场中的整体广场总和
Sums of Integral Squares In Certain Complex Bi-quadratic Fields
论文作者
论文摘要
令K为代数数字字段，O_K为其整数环。令S_K为O_K中的元素集，它是O_K和S（O_K）中的正方形总和（o_k）表示代表-1in O_K所需的最小平方数。令G（s_k）为最小的正整数t，以使s_k中的每个元素都是O_K中的t squares的总和。这里的k在M and -n的平方根上生成了理性数的字段，其中m一致3 mod 4和n一致1 mod 4是两个不同的正方形无正方形无正方形整数，我们证明$ s_k = o_k。我们还证明G（O_K）少或等于S（O_K）+1或S（O_K）+2。应用此信息，我们表明，如果s（o_k）= 2，则g（o_k）= 3。这项工作是Zhang和Ji最近发起的一项研究的延续。
Let K be an algebraic number field and O_K be its ring of integers. Let S_K be the set of elements in O_K which are sums of squares in O_K and s(O_K) the minimal number of squares necessary to represent -1in O_K. Let g( S_K ) be the smallest positive integer t such that every element in S_K is a sum of t squares in O_K. Here K is generated over field of rational number by square root of m and -n , where m congruent 3 mod 4 and n congruent 1 mod 4 are two distinct positive square free integers, we prove that $ S_K= O_K. We also prove that g(O_ K) less or equals to s(O_K)+1 or s(O_K)+2. Applying this, we shows that if s(O_K)=2, then g(O_K)=3. This work is continuation of a recent study initiated by Zhang and Ji .
