Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
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
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, 1288–1321, 1439 (Russian). MR 522940 (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 (11,230f)
  • 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 (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 (32 #5489a)
  • 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 (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: http://dx.doi.org/10.1090/S1061-0022-09-01078-4
PII: S 1061-0022(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