A Note on Sums of Squares in Non-Totally Real Fields

Let K be any non-totally real number field and \(\mathcal {O}_K\) be its ring of integers. Let \(m_K\) be the smallest positive integer such that every element of \(m_K \mathcal {O}_K \) can be written as sums of integral squares. We have shown that \(m_K \le 4\) .