Mots-clés : residue inverse.
@article{SM_2022_213_2_a3,
author = {M. A. Korolev},
title = {Vinogradov's sieve and an estimate for an incomplete {Kloosterman} sum},
journal = {Sbornik. Mathematics},
pages = {216--234},
year = {2022},
volume = {213},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2022_213_2_a3/}
}
M. A. Korolev. Vinogradov's sieve and an estimate for an incomplete Kloosterman sum. Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 216-234. http://geodesic.mathdoc.fr/item/SM_2022_213_2_a3/
[1] A. Weil, “On some exponential sums”, Proc. Nat. Acad. Sci. U.S.A., 34:5 (1948), 204–207 | DOI | MR | Zbl
[2] A. Weil, Basic number theory, Grundlehren Math. Wiss., 144, 3rd ed., Springer-Verlag, New York–Berlin, 1974, xviii+325 pp. | MR | MR | Zbl | Zbl
[3] A. A. Karatsuba, “The distribution of inverses in a residue ring modulo a given modulus”, Russian Acad. Sci. Dokl. Math., 48:3 (1994), 452–454 | MR | Zbl
[4] A. A. Karatsuba, “Fractional parts of functions of a special form”, Izv. Math., 59:4 (1995), 721–740 | DOI | MR | Zbl
[5] A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981 | DOI | MR | Zbl
[6] A. A. Karatsuba, “Analogi nepolnykh summ Kloostermana i ikh prilozheniya”, Tatra Mt. Math. Publ., 11 (1997), 89–120 | MR | Zbl
[7] A. A. Karatsuba, “Kloosterman double sums”, Math. Notes, 66:5 (1999), 565–569 | DOI | DOI | MR | Zbl
[8] A. A. Karatsuba, “Sums of fractional parts of functions of a special form”, Dokl. Math., 54:1 (1996), 541 | MR | Zbl
[9] M. A. Korolev, “Incomplete Kloosterman sums and their applications”, Izv. Math., 64:6 (2000), 1129–1152 | DOI | DOI | MR | Zbl
[10] M. A. Korolev, “Short Kloosterman sums with weights”, Math. Notes, 88:3 (2010), 374–385 | DOI | DOI | MR | Zbl
[11] J. Bourgain, M. Z. Garaev, “Sumsets of reciprocals in prime fields and multilinear Kloosterman sums”, Izv. Math., 78:4 (2014), 656–707 | DOI | DOI | MR | Zbl
[12] M. A. Korolev, “On short Kloosterman sums modulo a prime”, Math. Notes, 100:6 (2016), 820–827 | DOI | DOI | MR | Zbl
[13] M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158 | DOI | DOI | MR | Zbl
[14] M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659 | DOI | DOI | MR | Zbl
[15] I. M. Vinogradov, “Novaya otsenka odnoi summy, soderzhaschei prostye chisla”, Matem. sb., 2(44):5 (1937), 783–792 | Zbl
[16] I. M. Vinogradov, “Raspredelenie kvadratichnykh vychetov i nevychetov vida $p+k$ po prostomu modulyu”, Matem. sb., 3(45):2 (1938), 311–319 | Zbl
[17] I. M. Vinogradov, “Nekotorye obschie lemmy i ikh primenenie k otsenke trigonometricheskikh summ”, Matem. sb., 3(45):3 (1938), 435–471 | Zbl
[18] I. M. Vinogradov, “Novaya otsenka odnoi trigonometricheskoi summy, soderzhaschei prostye chisla”, Izv. AN SSSR. Ser. matem., 2:1 (1938), 3–14 | Zbl
[19] I. M. Vinogradov, “Uluchshenie otsenki odnoi trigonometricheskoi summy, soderzhaschei prostye chisla”, Izv. AN SSSR. Ser. matem., 2:1 (1938), 15–24 | Zbl
[20] I. M. Vinogradov, “Otsenka nekotorykh summ, soderzhaschikh prostye chisla”, Izv. AN SSSR. Ser. matem., 2:4 (1938), 399–416 | Zbl
[21] I. M. Vinogradov, “Utochnenie metoda otsenki summ s prostymi chislami”, Izv. AN SSSR. Ser. matem., 7:1 (1943), 17–34 | MR | Zbl
[22] I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Interscience Publishers, London–New York, 1954, x+180 pp. | MR | MR | Zbl | Zbl
[23] I. M. Vinogradov, Izbrannye trudy, Izd-vo AN SSSR, M., 1952, 436 pp. | MR | Zbl
[24] I. M. Vinogradov, “An estimate for a certain sum extended over the primes of an arithmetical progression”, Amer. Math. Soc. Transl. Ser. 2, 82, Amer. Math. Soc., Providence, RI, 1969, 147–164 | DOI | MR | Zbl
[25] I. M. Vinogradov, “Special variants of the method of trigonometric sums”, Selected works, Section III, Springer-Verlag, Berlin, 1985 | MR | MR | Zbl | Zbl
[26] G. Tenenbaum, Introduction to analytic and probabilistic number theory, Cambridge Stud. Adv. Math., 46, Cambridge Univ. Press, Cambridge, 1995, xvi+448 pp. | MR | Zbl