The product of symbols of $p^n$th power residues as an Abelian integral
The product of symbols of $p^n$th power residues as an Abelian integral
In accordance with the Hilbert–Shafarevich ideology, the reciprocity law must be an analog of an integral theorem asserting that the Abelian integral of a differential form on a Riemann surface is equal to the sum of residues at singular points. In the present paper, it is shown that the product …