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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)
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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 $p_1$ and $p_2$ and the cube of a natural number $m$ satisfying the conditions $|p_i-N/3|\le H$, $|m^3-N/3|\le H$, $H\ge N^{5/6}\mathscr L^{10}$.
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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    • This publication is cited in the following 6 articles:
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