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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
Published electronically: October 1, 2009
MathSciNet review: 2530895
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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. Šafarevič, A general reciprocity law, Mat. Sbornik N.S. 26(68) (1950), 113–146 (Russian). MR 0031944
  • 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. David Hilbert, Gesammelte Abhandlungen. Erster Band. Zahlentheorie, Chelsea Publishing Co., New York, 1965 (German). MR 0188046
  • 7. I. B. Fesenko and S. V. Vostokov, Local fields and their extensions, Translations of Mathematical Monographs, vol. 121, American Mathematical Society, Providence, RI, 1993. A constructive approach; With a foreword by I. R. Shafarevich. MR 1218392

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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

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

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