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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 3, Pages 475–483 (Mi izv2306)  

This article is cited in 14 scientific papers (total in 16 papers)

Uniform approximation of the remainder term in the Dirichlet divisor problem

A. A. Karatsuba


Abstract: In this paper we study the average value of the function $\tau_k(n)$, the number of representations of $n$ as a product of $k$ natural factors, $n\leqslant x$, with a remainder term which is uniform in $x$ and $k$.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:3, 467–475

Bibliographic databases:

UDC: 511.26
MSC: Primary 10H25; Secondary 10H05
Received: 11.01.1972

Citation: A. A. Karatsuba, “Uniform approximation of the remainder term in the Dirichlet divisor problem”, Izv. Akad. Nauk SSSR Ser. Mat., 36:3 (1972), 475–483; Math. USSR-Izv., 6:3 (1972), 467–475

Citation in format AMSBIB
\Bibitem{Kar72}
\by A.~A.~Karatsuba
\paper Uniform approximation of the remainder term in the Dirichlet divisor problem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 3
\pages 475--483
\mathnet{http://mi.mathnet.ru/izv2306}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318077}
\zmath{https://zbmath.org/?q=an:0239.10025}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 3
\pages 467--475
\crossref{https://doi.org/10.1070/IM1972v006n03ABEH001883}


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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. V. A. Plaksin, “An asymptotic formula for the number of solutions of a nonlinear equation with prime numbers”, Math. USSR-Izv., 18:2 (1982), 275–348  mathnet  crossref  mathscinet  zmath
    2. E. I. Panteleeva, “A brief contribution to the question of the divisor problem”, Math. Notes, 53:4 (1993), 454–457  mathnet  crossref  mathscinet  zmath  isi  elib
    3. E. I. Panteleeva, “On the mean values of certain arithmetic functions”, Math. Notes, 55:2 (1994), 178–184  mathnet  crossref  mathscinet  zmath  isi  elib
    4. A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981  mathnet  crossref  mathscinet  zmath  isi
    5. A. A. Karatsuba, “On a certain arithmetic function”, Russian Math. Surveys, 50:5 (1995), 1088–1089  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. G. I. Arkhipov, V. I. Blagodatskikh, V. S. Vladimirov, S. M. Voronin, O. B. Lupanov, E. F. Mishchenko, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, “Anatolii Alekseevich Karatsuba (on his 60th birthday)”, Russian Math. Surveys, 53:2 (1998), 419–422  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. A. Karatsuba, “Weighted character sums”, Izv. Math., 64:2 (2000), 249–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. A. Karatsuba, “On the Relationship between the Multidimensional Dirichlet Divisor Problem and the Boundary of Zeros of $\zeta(s)$”, Math. Notes, 70:3 (2001), 432–435  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. M. E. Changa, “On sums of multiplicative functions over numbers all of whose prime divisors belong to given arithmetic progressions”, Izv. Math., 69:2 (2005), 423–438  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. O. V. Kolpakova, “New Estimates of the Remainder in an Asymptotic Formula in the Multidimensional Dirichlet Divisor Problem”, Math. Notes, 89:4 (2011), 504–518  mathnet  crossref  crossref  mathscinet  isi
    12. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    13. Fedorov G.V., “Ob odnoi teoreme a.i. pavlova”, Doklady akademii nauk, 446:3 (2012), 269–269  elib
    14. K. M. Eminyan, “The generalized divisor problem with natural numbers of a special form”, Sb. Math., 206:7 (2015), 1020–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. K. M. Eminyan, “Obobschennaya problema delitelei s naturalnymi chislami, imeyuschimi dvoichnye razlozheniya spetsialnogo vida”, Chebyshevskii sb., 17:1 (2016), 270–283  mathnet  elib
    16. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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