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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
@article{AA_2008_20_6_a2,
     author = {S. V. Vostokov},
     title = {The classical reciprocity law for power residues as an analog of the {Abelian} integral theorem},
     journal = {Algebra i analiz},
     pages = {108--118},
     publisher = {mathdoc},
     volume = {20},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2008_20_6_a2/}
}
TY  - JOUR
AU  - S. V. Vostokov
TI  - The classical reciprocity law for power residues as an analog of the Abelian integral theorem
JO  - Algebra i analiz
PY  - 2008
SP  - 108
EP  - 118
VL  - 20
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2008_20_6_a2/
LA  - ru
ID  - AA_2008_20_6_a2
ER  - 
%0 Journal Article
%A S. V. Vostokov
%T The classical reciprocity law for power residues as an analog of the Abelian integral theorem
%J Algebra i analiz
%D 2008
%P 108-118
%V 20
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2008_20_6_a2/
%G ru
%F AA_2008_20_6_a2
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