Geodesic
On the function $G(n)$ in Waring's problem
Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 239-249

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Using a $p$-adic method, the author obtains a new estimate for the Hardy–Littlewood function $G(n)$: $G(n)2n\log n+2n\log\log n+12n$. Bibliography: 18 titles. 
@article{IM2_1986_27_2_a2,
     author = {A. A. Karatsuba},
     title = {On the function $G(n)$ in {Waring's} problem},
     journal = {Izvestiya. Mathematics },
     pages = {239--249},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a2/}
}
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A. A. Karatsuba. On the function $G(n)$ in Waring's problem. Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 239-249. http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a2/