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Chebyshevskii Sbornik, 2015, Volume 16, Issue 1, Pages 232–247 (Mi cheb378)  

This article is cited in 3 scientific papers (total in 4 papers)

INTERNATIONAL CONFERENCE IN MEMORY OF A. A. KARATSUBA ON NUMBER THEORY AND APPLICATIONS

Short Weyl sums and their applications

Z. Kh. Rakhmonov, N. N. Nazrubloev, A. O. Rakhimov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
Full-text PDF (324 kB) Citations (4)
References:
Abstract: We shall study the behavior of short Weyl sums of the form
T(α,x,y)=xy<mxe(αmn)
on major arcs and obtain an asymptotic formula for the number of representations of a sufficiently large positive integer N as a sum of 33 fifth powers of positive integers xi, that satisfy |xi(N33)15|H, HN151340+ε.
Bibliography: 17 titles.
Keywords: Short Weyl sums, Almost equal summands, Circle metods, Waring's problem.
Received: 16.02.2015
Bibliographic databases:
Document Type: Article
UDC: 511.524
Language: Russian
Citation: Z. Kh. Rakhmonov, N. N. Nazrubloev, A. O. Rakhimov, “Short Weyl sums and their applications”, Chebyshevskii Sb., 16:1 (2015), 232–247
Citation in format AMSBIB
\Bibitem{RakNazRah15}
\by Z.~Kh.~Rakhmonov, N.~N.~Nazrubloev, A.~O.~Rakhimov
\paper Short Weyl sums and their applications
\jour Chebyshevskii Sb.
\yr 2015
\vol 16
\issue 1
\pages 232--247
\mathnet{http://mi.mathnet.ru/cheb378}
\elib{https://elibrary.ru/item.asp?id=23384587}
Linking options:
  • https://www.mathnet.ru/eng/cheb378
  • https://www.mathnet.ru/eng/cheb/v16/i1/p232
  • This publication is cited in the following 4 articles:
    1. Z. Kh. Rakhmonov, F. Z. Rakhmonov, “Asimptoticheskaya formula v probleme Varinga s pochti proportsionalnymi slagaemymi”, Chebyshevskii sb., 25:2 (2024), 139–168  mathnet  crossref
    2. Z. Kh. Rakhmonov, “Obobschenie problemy Varinga dlya devyati pochti proportsionalnykh kubov”, Chebyshevskii sb., 24:3 (2023), 71–94  mathnet  crossref
    3. Z. Kh. Rakhmonov, I. Allakov, B. Kh. Abraev, “Obobschenie ternarnoi problemy Goldbakha s pochti ravnymi slagaemymi”, Chebyshevskii sb., 24:4 (2023), 264–298  mathnet  crossref
    4. E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, V. N. Chubarikov, “O konferentsii pamyati Anatoliya Alekseevicha Karatsuby po teorii chisel i prilozheniyam”, Chebyshevskii sb., 16:1 (2015), 89–152  mathnet  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:347
    Full-text PDF :126
    References:62
     
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