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The classical reciprocity law for power residues as an analog of the Abelian integral theorem
Author(s):
S.
V.
Vostokov
Translated by:
B. M. Bekker
Original publication:
Algebra i Analiz,
tom 20
(2008),
nomer 6.
Journal:
St. Petersburg Math. J.
20
(2009),
929-936.
MSC (2000):
Primary 11R37
Posted:
October 1, 2009
MathSciNet review:
2530895
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Additional information
Abstract:
A formula for power residue symbols is deduced, which can be treated as an analog of the Abelian integral theorem for number fields.
References:
-
- 1.
- S. V. Vostokov, An explicit form of the reciprocity law, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), no. 6, 1288-1320; English transl., Math. USSR-Izv. 13 (1978), no. 3, 557-588 (1979). MR 0522940 (80f:12014)
- 2.
- A. N. Parshin, The way. Mathematics and other worlds, Dobrosvet, Moscow, 2002. (Russian)
- 3.
- I. R. Shafarevich, A general reciprocity law, Mat. Sb. 26(68) (1950), no. 1, 113-146; English transl., Amer. Math. Soc. Transl. Ser. 2, vol. 4, Amer. Math. Soc., Providence, RI, 1956, pp. 73-106. MR 0031944 (11:230f)
- 4.
- H. Brückner, Explizites Reziprozitätsgesetz und Anwendungen, Vorlesungen Fachbereich Math. Univ. Essen, No. 2, Univ. Essen, Essen, 1979. MR 0533354 (80m:12015)
- 5.
- H. Hasse, Die Normenresttheorie relativ-Abelscher Zahlkoerper als Klassenkoerpertheorie im Kleinen, J. Reine Angew. Math. 162 (1930), 145-168.
- 6.
- D. Hilbert, Gesammelte Abhandlungen. Bd. 1: Zahlentheorie, Springer, Berlin, 1932. MR 0188046 (32:5489a)
- 7.
- I. Fesenko and S. Vostokov, Local fields and their extensions, Transl. Math. Monogr., vol. 121, Amer. Math. Soc., Providence, RI, 1993. MR 1218392 (94d:11095)
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Additional Information:
S.
V.
Vostokov
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Petrodvorets, 198504 St. Petersburg, Russia
Email:
sergei.vostokov@gmail.com
DOI:
10.1090/S1061-0022-09-01078-4
PII:
S 1061-0022(09)01078-4
Keywords:
Power residue symbol,
reciprocity law
Received by editor(s):
14/APR/2008
Posted:
October 1, 2009
Additional Notes:
Supported by INTAS, SFB-478 ``Algebraische Strukturen'', and RFBR (grant no. 08-01-00777-a).
Copyright of article:
Copyright
2009,
American Mathematical Society
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