Geodesic
The~exponent of~convergence of~a~special integral in~multidimensional problems Terry
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 74-103.

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

In the present article new lower and upper bounds for the convergence exponent of the special integral of Tarry's problem are proven. The question on convergence is solved for a wide class of polynomials.
Keywords: Tarry's problem, special integral, convergence exponent, system of diophantine equations, Gram determinant, surface integrals. 
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Ilgar Shikar oglu Jabbarov. The~exponent of~convergence of~a~special integral in~multidimensional problems Terry. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 74-103. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a6/

[1] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1971 | MR

[2] Vinogradov I. M., Karatsuba A. A., “Metod trigonometricheskikh summ v teorii chisel”, Tr. MIAN SSSR, 168, 1984, 4–30 | MR | Zbl

[3] Hua Loo Keng, “On the number of solutions of Tarry`s problem”, Acta Sci. Sinica, 1:1 (1952), 1–76 | MR

[4] Chubarikov V. N., “O kratnykh ratsionalnykh trigonometricheskikh summakh i kratnykh integralakh”, Matematicheskie zametki, 20:1 (1976), 61–68 | MR | Zbl

[5] Chubarikov V. N., “O kratnom trigonometricheskom integrale”, Doklady AN SSSR, 227:6 (1976), 1308–1310 | MR | Zbl

[6] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Trigonometricheskie integraly”, Izv. AN SSSR. Ser. mat., 43:5 (1979), 971–1003 | MR

[7] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Pokazatel skhodimosti osobogo integrala problemy Terri”, Doklady AN SSSR. Ser. Mat., 248:2 (1979), 268–272 | MR | Zbl

[8] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy i ikh prilozheniya”, Tr. MIAN SSSR, 151, 1980, 1–128

[9] Chubarikov V. N., “Ob asimptoticheskikh formulakh dlya integrala I. M. Vinogradova i ego obobschenii”, Tr. MIAN SSSR, 157, 1981, 214–232 | MR | Zbl

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

[11] Dzhabbarov I. Sh., “Ob odnom tozhdestve garmonicheskogo analiza i ego prilozheniyakh”, Doklady AN SSSR, 314:5 (1990), 1052–1054 | Zbl

[12] Dzhabbarov I. Sh., “Ob otsenkakh trigonometricheskikh integralov”, Tr. MIAN, 207 (1994), 82–92 | Zbl

[13] Dzhabbarov I. Sh., “Ob otsenkakh trigonometricheskikh integralov”, Chebyshevskii sbornik, 11:1(33) (2010), 85–108 | MR | Zbl

[14] Dzhabbarov I. Sh., “O pokazatele skhodimosti osobogo integrala dvumernoi problemy Terri”, Uchenye zapiski Orlovskogo gos. un-ta, 2012, no. 6(50)

[15] Gantmakher F. R., Teoriya matrits, Nauka, M., 1954 | MR

[16] Kurant R., Kurs differentsialnogo i integralnogo ischisleniya, Nauka, M., 1970

[17] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984 | MR | Zbl

[18] Shilov G. E., Matematicheskii analiz. Funktsii neskolkikh veschestvennykh peremennykh, Nauka, M., 1972 | Zbl

[19] Voevodin V. V., Lineinaya algebra, Nauka, M., 1974 | MR | Zbl

[20] Lankaster P., Teoriya matrits, Nauka, M., 1978 | MR

[21] Nikolskii S. M., Kurs matematicheskogo analiza, v. 1, 4-e izd., Nauka, M., 1990 | MR

[22] Nikolskii S. M., Kurs matematicheskogo analiza, v. 2, 4-e izd., Nauka, M., 1991 | MR

[23] Arkhipov G. I., Sadovnichii V. A., Chubarikov V. N., Lektsii po matematicheskomu analizu, Vysshaya shkola, M., 1999, 695 pp.

[24] Gelfand I. M., Lektsii po lineinei algebre, Nauka, M., 1971 | MR

[25] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 1979

[26] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1976 | MR

[27] Landau E., Vvedenie v differentsialnoe i integralnoe ischislenie, GIIL, M., 1948

[28] Rudin U., Osnovy matematicheskogo analiza, Mir, M., 1976

[29] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, 2-e izd., Nauka, M., 1968