Geodesic
On~Waring's problem with nonintegral exponent
Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 443-454

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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. 
@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},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a1/}
}
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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/