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

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

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. 
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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/

[1] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, 2-e izd., Nauka, M., 1980 | MR

[2] Vinogradov I. M., “K voprosu o verkhnei granitse dlya $G(n)$”, Izv. AN SSSR. Ser. matem., 23:5 (1959), 637–642 | MR | Zbl

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

[4] Vinogradov I. M., “Novaya otsenka $G(n)$ v probleme Varinga”, Dokl. AN SSSR, 4:5–6 (1934), 249–253 | Zbl

[5] Vinogradov I. M., “O verkhnei granitse $G(n)$ v probleme Varinga”, Izv. AN SSSR, 1934, no. 10, 1455–1469

[6] Vaughan R. C., The Hardy–Littlewood method, Cambridge, 1981 | MR

[7] Karatsuba A. A., “Problema Varinga dlya sravneniya po modulyu, ravnomu stepeni prostogo chisla”, Vestnik MGU, 1:4 (1962), 28–38 | MR

[8] Karatsuba A. A., “Trigonometricheskie summy spetsialnogo vida i ikh prilozheniya”, Izv. AN SSSR. Ser. matem., 28:1 (1964), 237–248 | Zbl

[9] Karatsuba A. A., “O sistemakh sravnenii”, Izv. AN SSSR. Ser. matem., 29:4 (1965), 935–944 | Zbl

[10] Karatsuba A. A., “Ob otsenke chisla reshenii nekotorykh uravnenii”, Dokl. AN SSSR, 165:1 (1965), 31–32 | Zbl

[11] Karatsuba A. A., “Sistemy sravnenii i uravneniya varingovskogo tipa”, Dokl. AN SSSR, 165:2, 274–276 | Zbl

[12] Karatsuba A. A., “Teoremy o srednem i polnye trigonometricheskie summy”, Izv. AN SSSR. Ser. matem., 30:1 (1966), 183–206 | Zbl

[13] Karatsuba A. A., “O nekotorykh arifmeticheskikh zadachakh s chislami, imeyuschimi malye prostye deliteli”, Acta Arithm., 27 (1975), 489–492 | Zbl

[14] Karatsuba A. A., “Trigonometricheskie summy i ikh primeneniya”, Trudy MKM, 1, Vankuver, 1975, 365–368 | Zbl

[15] Karatsuba A. A., “Ob odnoi sisteme sravnenii”, Matem. zametki, 19:3 (1976), 389–392 | MR | Zbl

[16] Vaughan R. C., “A survey of some important problems in additive number theory”, Journées Arithmétiques de Luminy (Colloq. Internat. CNRS, Centre Univ. Luminy, Luminy, 1978), Astérisque, 61, Soc. Math. France, Paris, 1979, 213–222 | MR

[17] Bredikhin B. M., Grishina T. I., “Elementarnaya otsenka $G(n)$ v probleme Varinga”, Matem. zametki, 24:1 (1978), 7–18 | MR | Zbl

[18] Linnik Yu. V., “O summakh Veilya”, Matem. sb., 12 (1943), 28–39 | MR | Zbl