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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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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
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\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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This publication is cited in the following articles:
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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
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E. I. Panteleeva, “A brief contribution to the question of the divisor problem”, Math. Notes, 53:4 (1993), 454–457
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E. I. Panteleeva, “On the mean values of certain arithmetic functions”, Math. Notes, 55:2 (1994), 178–184
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A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981
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A. A. Karatsuba, “On a certain arithmetic function”, Russian Math. Surveys, 50:5 (1995), 1088–1089
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N. M. Timofeev, “An additive divisor problem with a growing number of factors”, Math. Notes, 61:3 (1997), 321–332
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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
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A. A. Karatsuba, “Weighted character sums”, Izv. Math., 64:2 (2000), 249–263
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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
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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
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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
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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
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Fedorov G.V., “Ob odnoi teoreme a.i. pavlova”, Doklady akademii nauk, 446:3 (2012), 269–269
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K. M. Eminyan, “The generalized divisor problem with natural numbers of a special form”, Sb. Math., 206:7 (2015), 1020–1029
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K. M. Eminyan, “Obobschennaya problema delitelei s naturalnymi chislami, imeyuschimi dvoichnye razlozheniya spetsialnogo vida”, Chebyshevskii sb., 17:1 (2016), 270–283
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M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43
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