Multidimensional problems in prime number theory
Čebyševskij sbornik, Tome 12 (2011) no. 4, pp. 174-263.

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

@article{CHEB_2011_12_4_a14,
     author = {V. N. Chubarikov},
     title = {Multidimensional problems in prime number theory},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {174--263},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a14/}
}
TY  - JOUR
AU  - V. N. Chubarikov
TI  - Multidimensional problems in prime number theory
JO  - Čebyševskij sbornik
PY  - 2011
SP  - 174
EP  - 263
VL  - 12
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a14/
LA  - ru
ID  - CHEB_2011_12_4_a14
ER  - 
%0 Journal Article
%A V. N. Chubarikov
%T Multidimensional problems in prime number theory
%J Čebyševskij sbornik
%D 2011
%P 174-263
%V 12
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a14/
%G ru
%F CHEB_2011_12_4_a14
V. N. Chubarikov. Multidimensional problems in prime number theory. Čebyševskij sbornik, Tome 12 (2011) no. 4, pp. 174-263. http://geodesic.mathdoc.fr/item/CHEB_2011_12_4_a14/

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

[2] I. M. Vinogradov, “Metod trigonometricheskikh summ v teorii chisel”, Trudy MIAN SSSR, XXIII, 1–109

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

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

[5] I. M. Vinogradov, “Novoe reshenii problemy Varinga”, DAN SSSR, 2:6 (1934), 337–341

[6] I. M. Vinogradov, “O nekotorykh novykh problemakh teorii chisel”, DAN SSSR, 3:1 (1934), 1–6 | MR | Zbl

[7] I. M. Vinogradov, “Nekotorye teoremy analiticheskoi teorii chisel”, DAN SSSR, 4:4 (1934), 185–187 | Zbl

[8] I. M. Vinogradov, “O priblizheniyakh posredstvom ratsionalnykh drobei, imeyuschikh znamenatelem tochnuyu stepen”, DAN SSSR, 2:1 (1935), 1–5 | Zbl

[9] I. M. Vinogradov, “O nekotorykh ratsionalnykh priblizheniyakh”, DAN SSSR, 3:1 (1935), 3–6 | Zbl

[10] I. M. Vinogradov, “Predstavlenie nechetnogo chisla summoi trekh prostykh chisel”, DAN SSSR, 15:6 (1937), 201–204

[11] I. M. Vinogradov, “Nekotorye obschie teoremy, otnosyaschiesya k teorii prostykh chisel”, Tr. Tbil. mat. in-ta, 3, 1938, 1–67

[12] I. M. Vinogradov, “Nekotorye problemy analiticheskoi teorii chisel”, Tr. Tretego Vsesoyuznogo matem. s'ezda (Moskva, 1958), v. 3, 3–13

[13] A. A. Karatsuba, “Problema Varinga dlya sravnenii po modulyu, ravnomu stepeni prostogo chisla”, Vestnik MGU, ser. I, 1962, 28–38 | Zbl

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

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

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

[17] A. A. Karatsuba, “Srednee znachenie modulya trigonometricheskoi summy”, Izv. AN SSSR. Ser. matem., 36:6 (1973) | MR

[18] A. A. Karatsuba, “Ob odnoi sisteme sravnenii”, Matem. zametki, 19:3 (1978), 389–392 | MR

[19] A. A. Karatsuba, “Sistemy sravnenii i uravneniya varingovskogo tipa”, DAN SSSR, 165:2 (1965), 274–276 | Zbl

[20] A. A. Karatsuba, “O trigonometricheskikh summakh”, DAN SSSR, 189:1 (1969), 31–34 | Zbl

[21] A. A. Karatsuba, “Raspredelenie proizvedenii sdvinutykh prostykh chisel v arifmeticheskikh progressiyakh”, DAN SSSR, 192:4 (1978), 724–727 | MR

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

[23] Landau E., Vorlesungen uber Zahlentheorie, v. 2, Leipzig, 1927

[24] Linnik Yu. V., “O vozmozhnosti edinogo metoda v nekotorykh voprosakh “additivnoi” i “distributivnoi” teorii prostykh chisel”, DAN SSSR, 49:1 (1945), 3–7 | MR | Zbl

[25] Linnik Yu. V., “Novoe dokazatelstvo teoremy Goldbakha–Vinogradova”, Mat. sb., 19:1 (1946), 3–8 | MR | Zbl

[26] Linnik Yu. V., “Otsenki summ Veilya po metodu I. M. Vinogradova”, Izv. AN SSSR. Ser. matem., 6:1 (1942), 41–70 | MR | Zbl

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

[28] Gelfond A. O., Linnik Yu. V., Elementarnye metody v analiticheskoi teorii chisel, Nauka, M., 1962

[29] Mardzhanishvili K. K., “Ob odnovremennom predstavlenii dvukh chisel summami $m$-ykh i $n$-ikh stepenei”, DAN SSSR, 2:6 (1936), 257–258

[30] Mardzhanishvili K. K., “Ob odnovremennom predstavlenii $n$ chisel summami polnykh pervykh, vtorykh, ..., $n$-kh stepenei”, Izv. AN SSSR. Ser. matem., 1 (1937), 609–601

[31] Mardzhanishvili K. K., “Ob odnoi sisteme diofantovykh uravnenii”, DAN SSSR, 22:11 (1939), 471–474

[32] Mardzhanishvili K. K., “Ob odnoi zadache additivnoi teorii chisel”, Izv. AN SSSR. Ser. matem., 1940, no. 4, 193–214 | Zbl

[33] Mardzhanishvili K. K., Issledovaniya po primeneniyu metoda trigonometricheskikh summ k additivnym zadacham, M., 1949

[34] Mardzhanishvili K. K., “Ob nekotorykh nelineinykh sistemakh uravnenii v tselykh chislakh”, Matem. sb., 33(75):3 (1953), 638–675

[35] Mardzhanishvili K. K., “Ob odnom osobom ryade”, Tr. MIAN, 142, 1976, 174–182

[36] Hilbert D., “Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl. $n$-ter Potenzen”, Math. Ann., 67 (1909), 281–300 | DOI | MR | Zbl

[37] Kamke E., “Verallgemeinerungen des Waring–Hilbertschen Satzen”, Math. Ann., 83 (1921), 8–38 | DOI | MR

[38] Hardy G. H., Ramanujan S., “Asymptotic formulae in combinatory analysis”, Proc. London Math. Soc., 17:2 (1918), 75–115 | DOI | MR

[39] Hardy G. H., Littlewood J. E., “A new solution of Waring's problem”, Gött. Nachr., 1920, 33–54 | Zbl

[40] I. M. Vinogradov, “Sur un theoreme general de Waring”, Mat. sb., 31 (1924), 490–507 ; 4 (1928), 393–400 | Zbl | Zbl

[41] I. M. Vinogradov, “O teoreme Varinga”, Izv. AN SSSR, OFMN, 1928, no. 4, 393–400 | Zbl

[42] I. M. Vinogradov, “Ob odnom klasse sovokupnykh diofantovykh uravnenii”, Izv. AN SSSR, OFMN, 1929, no. 4, 355–376 | Zbl

[43] Hardy G. H., Littlewood J. E., “The number $\Gamma (k)$ in Waring's problem”, Proc. London Math. Soc., 28 (1928), 518–542 | DOI | MR | Zbl

[44] Khua Lo-ken, “Additivnaya teoriya prostykh chisel”, Tr. MIAN, 22, 1947, 1–179

[45] Khua Lo-ken, Metod trigonometricheskikh summ i ego primeneniya v teorii chisel, Mir, M., 1964 | MR

[46] Hua Loo-keng, “On the number of silutions of Tarry's problem”, Acta sci. Sinica, 1:1 (1952), 1–75 | MR

[47] G. I. Arkhipov, “O znachenii osobogo ryada v probleme Gilberta–Kamke”, DAN SSSR, 259:2 (1981), 265–267 | MR | Zbl

[48] G. I. Arkhipov, “O probleme Gilberta–Kamke”, Izv. AN SSSR. Ser. matem., 48:1 (1984), 3–52 | MR | Zbl

[49] G. I. Arkhipov, Issledovanie po probleme Gilberta–Kamke, Doktorskaya dissertatsiya, M., 1984

[50] G. I. Arkhipov, “Kratnye trigonometricheskie summy”, DAN SSSR, 219:5 (1974), 1036–1037 | Zbl

[51] G. I. Arkhipov, “Teorema o srednem znachenii modulya kratnoi trigonometricheskoi summy”, Matem. zametki, 17:1 (1975), 143–153 | MR | Zbl

[52] G. I. Arkhipov, “Otsenki dvoinykh trigonometricheskikh summ G. Veilya”, Tr. MIAN, 142, 1976, 46–66

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

[54] G. I. Arkhipov, V. N. Chubarikov, “Kratnye trigonometricheskie summy”, Izv. AN SSSR, 40:1 (1976), 209–220 | MR | Zbl

[55] G. I. Arkhipov, A. A. Karautsba, V. N. Chubarikov, “Verkhnyaya granitsa modulya kratnoi trigonometricheskoi summy”, Tr. MIAN, 143, 1977, 3–31 | Zbl

[56] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Tochnaya otsenka chisla reshenii odnoi sistemy diaofantovykh uravnenii”, Izv. AN SSSR. Ser. matem., 1978, no. 6, 1187–1226 | MR | Zbl

[57] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Raspredelenie drobnykh dolei mnogochlenov ot neskolkikh peremennykh”, Matem. zam., 25:1 (1979), 3–14 | MR | Zbl

[58] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy”, Tr. MIAN, 151, 1980, 1–128 | MR

[59] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Ob odnoi sisteme diofantovykh uravnenii”, DAN SSSR, 252:2 (1980), 275–276 | MR | Zbl

[60] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Ravnomernee otsenki kratnykh trigonometricheskikh summ”, DAN SSSR, 252:6 (1980), 1289–1291 | MR | Zbl

[61] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy i ikh prilozheniya”, Izv. AN SSSR. Ser. matatem., 44:4 (1980), 723–881 | MR

[62] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Novye ravnomernye otsenki kratnykh trigonometricheskikh summ”, DAN SSSR, 272:1 (1983), 11–12 | MR | Zbl

[63] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Osobye sluchai teorii kratnykh trigonometricheskikh summ”, Izv. AN SSSR, 47:4 (1983), 707–784 | MR | Zbl

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

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

[66] Arkhipov G. I., Chubarikov V. N., “Ob arifmeticheskikh usloviyakh razreshimosti nelineinykh sistem diofantovykh uravnenii”, DAN SSSR, 284:1 (1985), 16–21 | MR | Zbl

[67] Chubarikov V. N., “Ob odnom kratnom trigonometricheskom integrale”, DAN SSSR, 227:6 (1976), 1308–1310 | MR | Zbl

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

[69] Chubarikov V. N., “Asimptoticheskaya formula srednego znacheniya kratnoi trigonometricheskoi summy”, Matem. zam., 23:6 (1978), 799–816 | MR | Zbl

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

[71] Chubarikov V. N., “Kratnye trigonometricheskie summy s prostymi chislami”, DAN SSSR, 278:2 (1984), 302–304 | MR | Zbl

[72] Chubarikov V. N., “Otsenki kratnykh trigonometricheskikh summ s prostymi chislami”, Izv. AN SSSR, 49:5 (1985), 1031–1067 | MR | Zbl

[73] Chubarikov V. N., “Ob odnovremennom predstavlenii naturalnykh chisel summami stepenei prostykh chisel”, DAN SSSR, 256:4 (1985), 525–591

[74] Arkhipov G. I., Karacuba A. A., Chubarikov V. N., “Multiple trigonometric sums”, Proc. of Steklov Institute of mathematics, 2, Amer. Math Soc., 1982, 1–126

[75] Chubarikov V. N., “Mnogomernaya additivnaya zadacha s prostymi chislami”, DAN SSSR, 1986, no. 4, 805–808 | MR