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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 322, Pages 149–175 (Mi znsl399)  
This article is cited in 7 scientific papers (total in 7 papers)

On Waring's problem (elementary methods)

Yu. V. Nesterenko

M. V. Lomonosov Moscow State University
Full-text PDF (294 kB) Citations (7)
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Abstract: The paper deals with two elementary methods for solving Waring's problem on the representation of numbers as a sum of equal exponents in powers of natural numbers. The first method is an elementary version of the original Hilbert's proof, and the second one simplifies and makes more precise the elementary Linnik's proof based on the estimation of the number of solutions of a certain system of Diophantine equations.
Received: 15.03.2005
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 137, Issue 2, Pages 4699–4715
DOI: https://doi.org/10.1007/s10958-006-0266-8
Bibliographic databases:
UDC: 519.68
Language: Russian
Citation: Yu. V. Nesterenko, “On Waring's problem (elementary methods)”, Proceedings on number theory, Zap. Nauchn. Sem. POMI, 322, POMI, St. Petersburg, 2005, 149–175; J. Math. Sci. (N. Y.), 137:2 (2006), 4699–4715
Citation in format AMSBIB
\Bibitem{Nes05}
\by Yu.~V.~Nesterenko
\paper On Waring's problem (elementary methods)
\inbook Proceedings on number theory
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 322
\pages 149--175
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl399}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2138457}
\zmath{https://zbmath.org/?q=an:1072.11073}
\elib{https://elibrary.ru/item.asp?id=9126053}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 137
\issue 2
\pages 4699--4715
\crossref{https://doi.org/10.1007/s10958-006-0266-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746170248}
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  • https://www.mathnet.ru/eng/znsl/v322/p149
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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