Hilbert Symbols (History) - Mathematics Stack Exchange
https://math.stackexchange.com:443/questions/3405505/hilbert-symbols-history
WebOct 23, 2019 · The "local part" introduces the Hilbert symbol $(a,b)_p$ which you cite, with arguments $a,b \in\mathbf Q_p^*$. By definition $(a,b)_p = +1$ if the quadratic form $z^2-ax^2-by^2$ represents $0$ in $\mathbf Q_p$ (i.e. admits a non zero isotropic vector), $-1$ if not. The point is that the Hilbert symbol can be explicitly given in terms of ...
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