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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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The classical reciprocity law for power residues as an analog of the Abelian integral theorem
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by S. V. Vostokov
Translated by: B. M. Bekker
St. Petersburg Math. J. 20 (2009), 929-936
DOI: https://doi.org/10.1090/S1061-0022-09-01078-4
Published electronically: October 1, 2009

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
  • S. V. Vostokov, An explicit form of the reciprocity law, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), no. 6, 1288–1321, 1439 (Russian). MR 522940
  • A. N. Parshin, The way. Mathematics and other worlds, Dobrosvet, Moscow, 2002. (Russian)
  • I. R. Šafarevič, A general reciprocity law, Mat. Sbornik N.S. 26(68) (1950), 113–146 (Russian). MR 0031944
  • H. Brückner, Explizites Reziprozitätsgesetz und Anwendungen, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen [Lecture Notes in Mathematics at the University of Essen], vol. 2, Universität Essen, Fachbereich Mathematik, Essen, 1979 (German). MR 533354
  • H. Hasse, Die Normenresttheorie relativ-Abelscher Zahlkoerper als Klassenkoerpertheorie im Kleinen, J. Reine Angew. Math. 162 (1930), 145–168.
  • David Hilbert, Gesammelte Abhandlungen. Erster Band. Zahlentheorie, Chelsea Publishing Co., New York, 1965 (German). MR 0188046
  • 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, DOI 10.1090/mmono/121
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Bibliographic 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
  • 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).
  • © Copyright 2009 American Mathematical Society
  • Journal: St. Petersburg Math. J. 20 (2009), 929-936
  • MSC (2000): Primary 11R37
  • DOI: https://doi.org/10.1090/S1061-0022-09-01078-4
  • MathSciNet review: 2530895