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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 281, Pages 5–34 (Mi znsl1487)  
This article is cited in 8 scientific papers (total in 8 papers)

Hilbert symbol in a complete multidimensional field for an arbitrary prime number. Part I

T. B. Belyaeva, S. V. Vostokov

Saint-Petersburg State University
Full-text PDF (326 kB) Citations (8)
Abstract: In the first part of this article we discuss two different definitions of Hilbert symbol and prove their equivalence.
The second part is devoted to the detailed consideration of the one-dimensional case for an arbitrary prime number $p$ (odd as well as even).
At the end of the article we give the explicit formulas in the general case of a multidimensional local field for the both different and mixed characteristic cases for an arbitrary prime number.
Received: 25.04.2001
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 120, Issue 4, Pages 1483–1500
DOI: https://doi.org/10.1023/B:JOTH.0000017880.47115.ae
Bibliographic databases:
UDC: 512.625
Language: Russian
Citation: T. B. Belyaeva, S. V. Vostokov, “Hilbert symbol in a complete multidimensional field for an arbitrary prime number. Part I”, Problems in the theory of representations of algebras and groups. Part 8, Zap. Nauchn. Sem. POMI, 281, POMI, St. Petersburg, 2001, 5–34; J. Math. Sci. (N. Y.), 120:4 (2004), 1483–1500
Citation in format AMSBIB
\Bibitem{BelVos01}
\by T.~B.~Belyaeva, S.~V.~Vostokov
\paper Hilbert symbol in a complete multidimensional field for an arbitrary prime number. Part~I
\inbook Problems in the theory of representations of algebras and groups. Part~8
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 281
\pages 5--34
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1487}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1875716}
\zmath{https://zbmath.org/?q=an:1118.11050}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 120
\issue 4
\pages 1483--1500
\crossref{https://doi.org/10.1023/B:JOTH.0000017880.47115.ae}
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  • https://www.mathnet.ru/eng/znsl/v281/p5
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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