Geodesic
On the generalized Hua problem
Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1149-1171.

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

We determine the precise value of the exponent of convergence of the improper integral $$ \gamma_1=\int _{\mathbb R^r}\biggl|\int_0^1e^{2\pi if(x)}\,dx\biggr|\,d\alpha_1\dots d\alpha_r, $$ where $f(x)=\alpha_1x^{C_1}+\dots+\alpha_rx^{C_r}$, $0$ are arbitrary real numbers. 
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A. Zrein. On the generalized Hua problem. Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1149-1171. http://geodesic.mathdoc.fr/item/IM2_1995_59_6_a2/

[1] Hua L. K., “On Tarry's problem”, Quart. J. Math., 9 (1938), 315–320 | DOI | Zbl

[2] Hua L. K., “On the number of solutions of Tarry's problem”, Acta Scientia Sinica, 1 (1952), 1–70 | MR

[3] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987 | MR

[4] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Tochnaya otsenka chisla reshenii odnoi sistemy diofantovykh uravnenii”, Izv. AN SSSR. Ser. matem., 42:6 (1978), 1187–1226 | MR | Zbl

[5] Zrein A., Osobye integraly v additivnykh zadachakh varingovskogo tipa, Dis. ...kand. fiz.-mat. nauk, Izd-vo MGU, M., 1993