Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

The classical reciprocity law for power residues as an analog of the Abelian integral theorem


Author: 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
DOI: https://doi.org/10.1090/S1061-0022-09-01078-4
Published electronically: October 1, 2009
MathSciNet review: 2530895
Full-text PDF

Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • 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)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 11R37

Retrieve articles in all journals with MSC (2000): 11R37


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: https://doi.org/10.1090/S1061-0022-09-01078-4
Keywords: Power residue symbol, reciprocity law
Received by editor(s): April 14, 2008
Published electronically: October 1, 2009
Additional Notes: Supported by INTAS, SFB-478 “Algebraische Strukturen”, and RFBR (grant no. 08-01-00777-a).
Article copyright: © Copyright 2009 American Mathematical Society

American Mathematical Society