Geodesic
Trigonometric integrals
Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 211-239.

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A number of theorems on bounds, some sharp, are obtained for trigonometric integrals, and estimates which can be applied to investigations of singular integrals in the Tarry problem and its generalizations are derived. Bibliography: 20 titles. 
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G. I. Arkhipov; A. A. Karatsuba; V. N. Chubarikov. Trigonometric integrals. Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 211-239. http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a0/

[1] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

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

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

[4] Hua L. K., “On the number of solutions of Tarry's problem”, Acta Scientia Sinica, 1 (1952), 1–76 | MR

[5] Khua Lo-ken, “O probleme Terri”, Tr. 3-go Vsesoyuzn. matem. s'ezda, IV, 1959, 140–143

[6] Mardzhanishvili K. K., “Ob odnovremennom predstavlenii chisel summami polnykh pervykh, vtorykh, ..., $n$-ykh stepenei”, Izv. AN SSSR. Ser. matem., 1 (1937), 609–631

[7] Mardzhanishvili K. K., “Ob odnoi sisteme uravnenii v prostykh chislakh”, Dokl. AN SSSR, 70 (1950), 381–383 | Zbl

[8] Mardzhanishvili K. K., “O nekotorykh nelineinykh sistemakh uravnenii v tselykh chislakh”, Matem. sb., 33 (1953), 630–675

[9] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Verkhnyaya granitsa modulya kratnoi trigonometricheskoi summy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 143, 1977, 3–31 | Zbl

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

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

[12] Hardy G. H., Littlewood J. E., “The trigonometrical series associated with elliptic $\theta$-function”, Acta Math., 37 (1914), 193–239 | DOI | MR | Zbl

[13] van der Corput J. G., “Zahlentheoretische Abschatzungen”, Math. Ann., 84 (1921), 57–79 | MR

[14] Titchmarsh E. C., “The lattice points in a circle”, Proc. Lond. Math. Soc. (2), 38 (1935), 96–115 | DOI

[15] Min S. H., “On the order $\zeta(1/2+it)$”, Trans. Amer. Soc., 65 (1949), 448–472 | DOI | MR | Zbl

[16] Titchmarsh E. K., Teoriya dzeta-funktsii Rimana, IL, M., 1953

[17] Sadikova S. M., “Nekotorye neravenstva dlya kharakteristicheskikh funktsii”, Teoriya veroyatn. i ee primen., 11 (1966), 500–506 | MR | Zbl

[18] Yurinskii V. V., “O primenenii lemmy van der Korputa dlya otsenki kharakteristicheskikh funktsii nekotorykh singulyarnykh raspredelenii”, Teoriya veroyatn. i ee primen., 16:2 (1971), 389–391 | Zbl

[19] Yurinskii V. V., “Otsenki kharakteristicheskikh funktsii nekotorykh vyrozhdennykh mnogomernykh raspredelenii”, Teoriya veroyatn. i ee primen., 17:1 (1972), 99–110 | MR

[20] Carleson L., Sjolin P., “Oscillatory integrals and a multiplier problem for the disc”, Studia Math., 44 (1972), 287–299 | MR | Zbl