Geodesic
A~new estimate for a~trigonometric integral of I.\,M.~Vinogradov
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 337-351.

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

This paper is devoted to refinements of I. M. Vinogradov's theorem on the mean. New estimates are obtained for the mean values of trigonometric sums which are effective on the domain of admissible variation of the parameters. Bibliography: 28 titles. 
@article{IM2_1988_30_2_a7,
     author = {O. V. Tyrina},
     title = {A~new estimate for a~trigonometric integral of {I.\,M.~Vinogradov}},
     journal = {Izvestiya. Mathematics },
     pages = {337--351},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a7/}
}
TY  - JOUR
AU  - O. V. Tyrina
TI  - A~new estimate for a~trigonometric integral of I.\,M.~Vinogradov
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 337
EP  - 351
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a7/
LA  - en
ID  - IM2_1988_30_2_a7
ER  - 
%0 Journal Article
%A O. V. Tyrina
%T A~new estimate for a~trigonometric integral of I.\,M.~Vinogradov
%J Izvestiya. Mathematics 
%D 1988
%P 337-351
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a7/
%G en
%F IM2_1988_30_2_a7
O. V. Tyrina. A~new estimate for a~trigonometric integral of I.\,M.~Vinogradov. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 337-351. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a7/

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

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

[3] Vinogradov I. M., “Novye otsenki summ Veilya”, Dokl. AN SSSR, 3:6 (1935), 195–198 | Zbl

[4] Vinogradov I. M., “A new method of extimation of trigonometrical sums”, Matem. sb. (nov. seriya), 1:2 (1936), 175–178

[5] Vinogradov I. M., “Nekotorye obschie lemmy i ikh primenenie k otsenke trigonometricheskikh summ”, Matem. sb. (nov. seriya), 3:3 (1938), 435–471 | Zbl

[6] Vinogradov I. M., “Ob otsenkakh trigonometricheskikh summ”, Dokl. AN SSSR, 34:7 (1942), 199–200

[7] Vinogradov I. M., “Obschie teoremy o verkhnei granitse modulya trigonometricheskoi summy”, Izv. AN SSSR. Ser. matem., 15:2 (1951), 109–130 | MR

[8] Vinogradov I. M., “Ob odnom kratnom integrale”, Izv. AN SSSR. Ser. matem., 22:5 (1958), 577–584 | MR | Zbl

[9] Vinogradov I. M., “K voprosu ob otsenke trigonometricheskikh summ”, Izv. AN SSSR. Ser. matem., 29:3 (1965), 493–504 | MR | Zbl

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

[11] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1975 | MR | Zbl

[12] Linnik Yu. V., “Otsenki summ Veilya”, Dokl. AN SSSR, 34:7 (1942), 201–203 | MR

[13] Linnik Yu. V., “O summakh Veilya”, Matem. sb., 12(54):1 (1943), 28–39 | MR | Zbl

[14] Karatsuba A. A., “Problema Varinga dlya sravneniya po modulyu, ravnomu stepeni prostogo chisla”, Vestnik MGU, ser. 1, 1962, no. 1, 28–38 | Zbl

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

[16] Karatsuba A. A., “Sistemy uravnenii i uravneniya varingovskogo tipa”, Dokl. AN SSSR, 165:2 (1965), 274–276 | Zbl

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

[18] Karatsuba A. A., “Ob odnoi sisteme neopredelennykh uravnenii”, Matem. zametki, 4:2 (1968), 125–128 | Zbl

[19] Karatsuba A. A., “Srednee znachenie modulya trigonometricheskoi summy”, Izv. AN SSSR. Ser. matem., 37:6 (1973), 1203–1227 | MR | Zbl

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

[21] Stechkin S. B., “O srednikh znacheniyakh modulya trigonometricheskoi summy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 134, 1975, 283–309 | Zbl

[22] Arkhipov G. I., “O srednem znachenii summ G. Veilya”, Matem. zametki, 23:6 (1978), 785–788 | MR | Zbl

[23] Arkhipov G. I., Chubarikov V. N., “O kratnykh trigonometricheskikh summakh”, Dokl. AN SSSR, 222:5 (1975), 1017–1019 | MR | Zbl

[24] Arkhipov G. I., Karatsuba A. A., “Novaya otsenka integrala I. M. Vinogradova”, Izv. AN SSSR. Ser. matem., 42:4 (1978), 751–762 | MR | Zbl

[25] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 151, 1980, 3–128 | MR | Zbl

[26] Sokolinskii V. Z., “O teoreme o srednem pri malom chisle peremennykh”, Izv. VGPI, 201 (1979), 45–55 | Zbl

[27] Von R., Metod Khardi–Littlvuda, Mir, M., 1985 | MR

[28] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 | MR