= Hasse invariant of a quadratic form
{c}
{title2=$\epsilon_v(q)=\prod_{i<j}(a_i,a_j)_v$}
For a nondegenerate diagonal <quadratic form> $q=\langle a_1,\ldots,a_m\rangle$, this product of <quadratic Hilbert symbols> is independent of diagonalization. Over a <p-adic field>, dimension, determinant square class and this invariant classify the form up to isometry. The product of the local invariants of a globally diagonalized form is one by the <Hilbert reciprocity law>; real places additionally record signature.
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