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Matematicheskie Zametki, 2014, Volume 95, Issue 3, Pages 445–456
DOI: https://doi.org/10.4213/mzm10204 (Mi mzm10204) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The Estermann Cubic Problem with Almost Equal Summands

Z. Kh. Rakhmonov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
Full-text PDF (514 kB) Citations (6)
References:
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DOI: https://doi.org/10.4213/mzm10204
Abstract: We prove an asymptotic formula for the number of representations of a sufficiently large natural number N as the sum of two primes p1 and p2 and the cube of a natural number m satisfying the conditions |pi−N/3|⩽H, |m3−N/3|⩽H, H⩾N5/6L10.
Keywords: Estermann cubic problem, prime, Weyl sum, Hua estimate, rational trigonometric sum, Poisson summation formula.
Received: 11.10.2012
English version:
Mathematical Notes, 2014, Volume 95, Issue 3, Pages 407–417
DOI: https://doi.org/10.1134/S0001434614030122
Bibliographic databases:
Document Type: Article
UDC: 511.24
Language: Russian
Citation: Z. Kh. Rakhmonov, “The Estermann Cubic Problem with Almost Equal Summands”, Mat. Zametki, 95:3 (2014), 445–456; Math. Notes, 95:3 (2014), 407–417
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm10204
  • https://doi.org/10.4213/mzm10204
  • https://www.mathnet.ru/eng/mzm/v95/i3/p445
    • This publication is cited in the following 6 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. P. Z. Rakhmonov, “The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands”, Math. Notes, 100:3 (2016), 438–447  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Z. Kh. Rakhmonov, N. N. Nazrublloev, A. O. Rakhimov, “Korotkie summy G. Veilya i ikh prilozheniya”, Chebyshevskii sb., 16:1 (2015), 232–247  mathnet  elib
    6. P. Z. Rakhmonov, “Obobschennaya ternarnaya problema Estermana dlya netselykh stepenei s pochti ravnymi slagaemymi”, Chebyshevskii sb., 16:1 (2015), 248–253  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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