Geodesic
The classical reciprocity law for power residues as an analog of the Abelian integral theorem
Algebra i analiz, Tome 20 (2008) no. 6, pp. 108-118.

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A formula for power residue symbols is deduced, which can be treated as an analog of the Abelian integral theorem for number fields.
Keywords: Power residue symbol, reciprocity law. 
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S. V. Vostokov. The classical reciprocity law for power residues as an analog of the Abelian integral theorem. Algebra i analiz, Tome 20 (2008) no. 6, pp. 108-118. http://geodesic.mathdoc.fr/item/AA_2008_20_6_a2/

[1] Vostokov S. V., “Yavnaya forma zakona vzaimnosti”, Izv. AN SSSR. Ser. mat., 42:6 (1978), 1288–1321 | MR | Zbl

[2] Parshin A. N., Put. Matematika i drugie miry, Dobrosvet, M., 2002

[3] Shafarevich I. R., “Obschii zakon vzaimnosti”, Mat. sb., 26(68):1 (1950), 113–146 | Zbl

[4] Brückner H., Explizites Reziprozitätsgesetz und Anwendungen, Vorlesungen Fachbereich Math. Univ. Essen, 2, Univ. Essen, Essen, 1979 | MR

[5] Hasse H., “Die Normenresttheorie relativ-Abelscher Zahlkoerper als Klassenkoerpertheorie im Kleinen”, J. Reine Angew. Math., 162 (1930), 145–168 | MR

[6] Hilbert D., Gesammelte Abhandlungen, Bd. 1, Springer, Berlin, 1932

[7] Fesenko I., Vostokov S., Local fields and their extensions, Transl. Math. Monogr., 121, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl