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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 6, Pages 1138–1150 (Mi izv1511)  

This article is cited in 1 scientific paper (total in 1 paper)

On Waring's problem with nonintegral exponent

G. I. Arkhipov, A. N. Zhitkov


Abstract: An asymptotic formula is obtained for representing a natural number $N$ by a sum of $k$ terms of the form $|x^c|$, where $k\ll n^2\ln n$. Here $x$ is a natural number and $c$ is a nonintegral real number greater than 2. The result of Deshouillers in which $k\ll n^3\ln n$ is also improved.
Bibliography: 9 titles.

Full text: PDF file (844 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:3, 443–454

Bibliographic databases:

UDC: 511.3
MSC: 10J06
Received: 01.06.1983

Citation: G. I. Arkhipov, A. N. Zhitkov, “On Waring's problem with nonintegral exponent”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984), 1138–1150; Math. USSR-Izv., 25:3 (1985), 443–454

Citation in format AMSBIB
\Bibitem{ArkZhi84}
\by G.~I.~Arkhipov, A.~N.~Zhitkov
\paper On~Waring's problem with nonintegral exponent
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 6
\pages 1138--1150
\mathnet{http://mi.mathnet.ru/izv1511}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=772109}
\zmath{https://zbmath.org/?q=an:0586.10028|0568.10027}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 443--454
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001295}


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    This publication is cited in the following articles:
    1. P. Z. Rakhmonov, “Short Sums with a Noninteger Power of a Natural Number”, Math. Notes, 95:5 (2014), 697–707  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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