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
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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. 
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     title = {On the number of summands in the asymptotic formula for the number of solutions to {Waring's} equation},
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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