Geodesic
On the number of summands in the asymptotic formula for the number of solutions to Waring's equation
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 285-296.

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

In the paper, an estimate of the number of summands in the asymptotic formula for the number of solutions to Waring's equation is obtained. This is achieved by means of a recurrent process leading to a greater reduction than that in Vinogradov's mean value theorem. 
@article{MZM_1998_64_2_a14,
     author = {A. V. Ustinov},
     title = {On the number of summands in the asymptotic formula for the number of solutions to {Waring's} equation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {285--296},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a14/}
}
TY  - JOUR
AU  - A. V. Ustinov
TI  - On the number of summands in the asymptotic formula for the number of solutions to Waring's equation
JO  - Matematičeskie zametki
PY  - 1998
SP  - 285
EP  - 296
VL  - 64
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a14/
LA  - ru
ID  - MZM_1998_64_2_a14
ER  - 
%0 Journal Article
%A A. V. Ustinov
%T On the number of summands in the asymptotic formula for the number of solutions to Waring's equation
%J Matematičeskie zametki
%D 1998
%P 285-296
%V 64
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a14/
%G ru
%F MZM_1998_64_2_a14
A. V. Ustinov. On the number of summands in the asymptotic formula for the number of solutions to Waring's equation. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 285-296. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a14/

[1] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980

[2] Bykovskii V. A., “O sistemakh neravenstv”, Zapiski nauch. sem. LOMI, 129, Nauka, L., 1981, 3–33 | MR

[3] Karatsuba A. A., “O sistemakh sravnenii”, Izv. AN SSSR. Ser. matem., 29 (1965), 935–944 | MR | Zbl