Algebraic Number Theory
《Algebraic Number Theory》 · 第 333 页 · Chapter V，Section 3「The Hilbert Symbol」
For a local field $K$ containing $\mu_n$, Kummer theory and class field theory define a nondegenerate bilinear pairing $K^*/K^{*n}\times K^*/K^{*n}\to\mu_n$; this pairing is called the Hilbert symbol.