The local Hilbert symbol is the multiplicativity defect of Maslov phases γ_v(a), and the product of these defects over all places equals 1, proving Hilbert reciprocity.
7, Springer, New York, 1973
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Reciprocity and the Maslov Phase
The local Hilbert symbol is the multiplicativity defect of Maslov phases γ_v(a), and the product of these defects over all places equals 1, proving Hilbert reciprocity.