Uniform approximation of the remainder term in the Dirichlet divisor problem
Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 467-475.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $k$.
@article{IM2_1972_6_3_a0,
     author = {A. A. Karatsuba},
     title = {Uniform approximation of the remainder term in the {Dirichlet} divisor problem},
     journal = {Izvestiya. Mathematics },
     pages = {467--475},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a0/}
}
TY  - JOUR
AU  - A. A. Karatsuba
TI  - Uniform approximation of the remainder term in the Dirichlet divisor problem
JO  - Izvestiya. Mathematics 
PY  - 1972
SP  - 467
EP  - 475
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a0/
LA  - en
ID  - IM2_1972_6_3_a0
ER  - 
%0 Journal Article
%A A. A. Karatsuba
%T Uniform approximation of the remainder term in the Dirichlet divisor problem
%J Izvestiya. Mathematics 
%D 1972
%P 467-475
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a0/
%G en
%F IM2_1972_6_3_a0
A. A. Karatsuba. Uniform approximation of the remainder term in the Dirichlet divisor problem. Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 467-475. http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a0/

[1] Dirichlet L., “Über die Bestimmung der mittleren Werte in der Zahlentheorie”, Abhand. Ak. Wiss. Berlin, 1849, 69–83; reprinted in Werke, 2, 49–66

[2] Voronoi G., “Sur un probléme du calcul des fonctions asymptotiques”, J. Math., 126 (1903), 241–282 | Zbl

[3] Landau E., “Über die Anzahl der Gitterpunkte in gewissen Bereichen”, Nachr. Königl. Gesell. Wiss. Gottingen, Math.-phys. Klassen, 6 (1912), 687–771

[4] Hardy G. H., Littlewood I. E., “The approximate functional equation in the theory of the zeta-function, with applications to the divisor problems of Dirichlet and Piltz”, Proc. London Math. Soc. (2), 21 (1922), 39–74 | DOI

[5] Mardzhanishvili K. K., “Otsenka odnoi arifmeticheskoi summy”, Dokl. AN SSSR, 22:7 (1939), 391–393

[6] Vinogradov I. M., “Novaya otsenka $\zeta(1+it)$”, Izv. AN CSCP. Ser. matem., 22 (1958), 161–164 | MR | Zbl

[7] Karatsuba A. A., “Otsenki trigonometricheskikh summ metodom I. M. Vinogradova i ikh primeneniya”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 112, 1971, 241–255 | Zbl

[8] Titchmarsh E. K., Teoriya dzeta-funktsii Rimana, IL, M., 1953