Geodesic
On Waring's problem with nonintegral exponent
Izvestiya. Mathematics, Tome 25 (1985) no. 3, pp. 443-454 
G. I. Arkhipov; A. N. Zhitkov. On Waring's problem with nonintegral exponent. Izvestiya. Mathematics, Tome 25 (1985) no. 3, pp. 443-454. http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a1/
@article{IM2_1985_25_3_a1,
     author = {G. I. Arkhipov and A. N. Zhitkov},
     title = {On~Waring's problem with nonintegral exponent},
     journal = {Izvestiya. Mathematics},
     pages = {443--454},
     year = {1985},
     volume = {25},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a1/}
}
TY  - JOUR
AU  - G. I. Arkhipov
AU  - A. N. Zhitkov
TI  - On Waring's problem with nonintegral exponent
JO  - Izvestiya. Mathematics
PY  - 1985
SP  - 443
EP  - 454
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a1/
LA  - en
ID  - IM2_1985_25_3_a1
ER  - 
%0 Journal Article
%A G. I. Arkhipov
%A A. N. Zhitkov
%T On Waring's problem with nonintegral exponent
%J Izvestiya. Mathematics
%D 1985
%P 443-454
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a1/
%G en
%F IM2_1985_25_3_a1

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

An asymptotic formula is obtained for representing a natural number $N$ by a sum of $k$ terms of the form $|x^c|$, where $k\ll n^2\ln n$. Here $x$ is a natural number and $c$ is a nonintegral real number greater than 2. The result of Deshouillers in which $k\ll n^3\ln n$ is also improved. Bibliography: 9 titles.

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

[2] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

[3] Vinogradov I. M., Osobye varianty metoda trigonometricheskikh summ, Nauka, M., 1976 | MR

[4] Segal B. I., “Teorema Varinga dlya stepenei s drobnymi i irratsionalnymi pokazatelyami”, Tr. fiz.-matem. in-ta im. V. A. Steklova AN SSSR, 5, 1934, 73–86 | Zbl

[5] Deshouillers J.-M., “Probleme de Waring avec exposants non entiers”, Bull. Soc. Math. France, 101:3 (1973), 285–295 | MR | Zbl

[6] Deshouillers J.-M., “Problème de Waring avec exposant non entier”, Séminaire Delange–Pisot–Poitou, 13e année (1971/72), Théorie des nombres, Fasc. 1, Exp. No. 4, Secrétariat Mathématique, Paris, 1973, 5 | MR

[7] Karatsuba A. A., “Ob odnoi zadache s prostymi chislami”, Dokl. AN SSSR, 259:6 (1981), 1291–1293 | MR | Zbl

[8] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1975 | MR | Zbl

[9] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Kratnye trigonometricheskie summy, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 151, 1980 | MR | Zbl