Non-decomposable quadratic forms over totally real number fields
Non-decomposable quadratic forms over totally real number fields
We give an upper bound for the norm of the determinant of non-decomposable totally positive quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find the lower and upper bounds for the minimal ranks of $n$-universal quadratic forms. For $\mathbb{Q}(\sqrt{2}),\mathbb{Q}(\sqrt{3}),\mathbb{Q}(\sqrt{5})$, $\mathbb{Q}(\sqrt{6})$, …