Geodesic
An additive divisor problem with a growing number of factors
Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 391-406 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\tau_k(n)$ be the number of representations of $n$ as the product of $k$ positive factors, $\tau_2(n)=\tau(n)$. The asymptotics of $\sum_{n\le x}\tau_k(n)\tau(n+1)$ for $80k^{10}(\ln\ln x)^3\le\ln x$ is shown to be uniform with respect to $k$. 
@article{MZM_1997_61_3_a7,
     author = {N. M. Timofeev},
     title = {An additive divisor problem with a~growing number of factors},
     journal = {Matemati\v{c}eskie zametki},
     pages = {391--406},
     year = {1997},
     volume = {61},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a7/}
}
TY  - JOUR
AU  - N. M. Timofeev
TI  - An additive divisor problem with a growing number of factors
JO  - Matematičeskie zametki
PY  - 1997
SP  - 391
EP  - 406
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a7/
LA  - ru
ID  - MZM_1997_61_3_a7
ER  - 
%0 Journal Article
%A N. M. Timofeev
%T An additive divisor problem with a growing number of factors
%J Matematičeskie zametki
%D 1997
%P 391-406
%V 61
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a7/
%G ru
%F MZM_1997_61_3_a7
N. M. Timofeev. An additive divisor problem with a growing number of factors. Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 391-406. http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a7/

[1] Linnik Yu. V., Dispersionnyi metod v binarnykh additivnykh zadachakh, Izd-vo LGU, L., 1961

[2] Motohashi Y., “On some additive problems”, J. Math. Soc. Japan, 28:4 (1976), 772–784 | DOI | MR | Zbl

[3] Motohashi Y., “An asymptotic series for an additive divisor problem”, Math. Z., 170 (1980), 43–63 | DOI | MR

[4] Karatsuba A. A., “Ravnomernaya otsenka ostatochnogo chlena v probleme delitelei Dirikhle”, Izv. AN SSSR. Ser. matem., 36 (1972), 475–483 | Zbl

[5] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1974

[6] Mardzhanishvili K. K., “Otsenka odnoi arifmeticheskoi summy”, Dokl. AN SSSR, 1939, no. 22, 391–393

[7] Montgomeri G., Multiplikativnaya teoriya chisel, Mir, M., 1974

[8] Timofeev N. M., “Problema Khardi i Litlvuda dlya chisel, imeyuschikh zadannoe chislo prostykh delitelei”, Izv. RAN. Ser. matem., 59:6 (1995), 181–206 | MR | Zbl

[9] Halberstam H., Richert H.-E., Sieve Methods, Acad. Press, London–N. Y., 1974 | Zbl