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. 
@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/}
}
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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/