The product of symbols of 𝑝ⁿth power residues as an Abelian integral

Ivanov, M.

doi:10.1090/S1061-0022-2013-01238-6

The product of symbols of $p^n$th power residues as an Abelian integral
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by M. A. Ivanov
Translated by: N. B. Lebedinskaya

St. Petersburg Math. J. 24 (2013), 275-281

DOI: https://doi.org/10.1090/S1061-0022-2013-01238-6

Published electronically: January 22, 2013

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Abstract:

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 of the symbols of $p^n$th power residues is the integral of a certain function.

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