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 Free Access

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, 1288–1321, 1439 (Russian). MR 522940
  • 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 aus dem Fachbereich Mathematik der Universität Essen [Lecture Notes in Mathematics at the University of Essen], vol. 2, Universität Essen, Fachbereich Mathematik, Essen, 1979 (German). MR 533354
  • 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
    David Hilbert, Gesammelte Abhandlungen. Zweiter Band. Algebra, Invariantentheorie, Geometrie, Chelsea Publishing Co., New York, 1965 (German). MR 0188047
    David Hilbert, Gesammelte Abhandlungen. Dritter Band. Analysis, Grundlagen der Mathematik, Physik, Verschiedenes, nebst einer Lebensgeschichte, Chelsea Publishing Co., New York, 1965 (German). MR 0188048
  • 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

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