Hilbert reciprocity law
= Hilbert reciprocity law
{c}
{title2=$\prod_v(a,b)_v=1$}
For nonzero $a,b$ in a <number field>, the product of their <quadratic Hilbert symbols> over all places is one. All but finitely many symbols are one. Over $\mathbb Q$, this is equivalent to quadratic reciprocity with its supplementary laws. It supplies the compatibility relation between the local invariants of a global quadratic form.