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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 6, Pages 181–206 (Mi izv58)  

This article is cited in 4 scientific papers (total in 5 papers)

The Hardy–Littlewood problem for numbers with a fixed number of prime divisors

N. M. Timofeev

Vladimir State Pedagogical University

Abstract: In this paper we investigate the number of representations of a natural number $N$ as the sum of a number with $k$ prime divisors and two squares, where $k$ may depend on $N$. We determine the asymptotic behaviour when $2\leqslant k\leqslant(2-\varepsilon)\ln\ln N$ and $(2+\varepsilon)\ln\ln N\leqslant k\leqslant b\ln\ln N$.

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English version:
Izvestiya: Mathematics, 1995, 59:6, 1283–1309

Bibliographic databases:

MSC: 11P55, 11D85, 11P32, 11N25
Received: 05.12.1994

Citation: N. M. Timofeev, “The Hardy–Littlewood problem for numbers with a fixed number of prime divisors”, Izv. RAN. Ser. Mat., 59:6 (1995), 181–206; Izv. Math., 59:6 (1995), 1283–1309

Citation in format AMSBIB
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\by N.~M.~Timofeev
\paper The Hardy--Littlewood problem for numbers with a~fixed number of prime divisors
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 6
\pages 181--206
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1481620}
\zmath{https://zbmath.org/?q=an:0878.11039}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 6
\pages 1283--1309
\crossref{https://doi.org/10.1070/IM1995v059n06ABEH000058}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UR47200009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Timofeev N., “Additive Problems with Numbers Having Given Amount of Prime Divisors”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1996, no. 6, 98–101  mathscinet  isi
    2. N. M. Timofeev, “An additive divisor problem with a growing number of factors”, Math. Notes, 61:3 (1997), 321–332  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. A. Zhukova, “The Hardy–Littlewood problem”, Russian Math. (Iz. VUZ), 44:2 (2000), 39–47  mathnet  mathscinet  zmath  elib
    4. G. I. Arkhipov, V. G. Zhuravlev, V. A. Iskovskikh, A. A. Karatsuba, M. B. Levina-Khripunova, V. N. Chubarikov, A. A. Yudin, “Nikolai Mikhailovich Timofeev (obituary)”, Russian Math. Surveys, 58:4 (2003), 773–776  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. N. M. Timofeev, M. B. Khripunova, “The Concentration Function of Additive Functions with Special Weight”, Math. Notes, 76:2 (2004), 244–263  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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