On Short Kloosterman Sums Modulo a Prime
Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 838-846.

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

Using the Karatsuba method, we obtain new estimates for Kloosterman sums modulo a prime, which, under certain constraints on the number of summands, are sharper than similar estimates found earlier.
Keywords: Kloosterman sum, Karatsuba method, inverse quantities.
@article{MZM_2016_100_6_a5,
     author = {M. A. Korolev},
     title = {On {Short} {Kloosterman} {Sums} {Modulo} a {Prime}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {838--846},
     publisher = {mathdoc},
     volume = {100},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a5/}
}
TY  - JOUR
AU  - M. A. Korolev
TI  - On Short Kloosterman Sums Modulo a Prime
JO  - Matematičeskie zametki
PY  - 2016
SP  - 838
EP  - 846
VL  - 100
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a5/
LA  - ru
ID  - MZM_2016_100_6_a5
ER  - 
%0 Journal Article
%A M. A. Korolev
%T On Short Kloosterman Sums Modulo a Prime
%J Matematičeskie zametki
%D 2016
%P 838-846
%V 100
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a5/
%G ru
%F MZM_2016_100_6_a5
M. A. Korolev. On Short Kloosterman Sums Modulo a Prime. Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 838-846. http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a5/

[1] A. A. Karatsuba, “Raspredelenie obratnykh velichin v koltse vychetov po zadannomu modulyu”, Dokl. RAN, 333:2 (1993), 138–139 | MR | Zbl

[2] A. A. Karatsuba, “Drobnye doli spetsialnogo vida funktsii”, Izv. RAN. Ser. matem., 59:4 (1995), 61–80 | MR | Zbl

[3] A. A. Karatsuba, “Analogi summ Kloostermana”, Izv. RAN. Ser. matem., 59:5 (1995), 93–102 | MR | Zbl

[4] A. A. Karatsuba, “Summy drobnykh dolei spetsialnogo vida funktsii”, Dokl. RAN, 349:3 (1996), 302 | MR | Zbl

[5] A. A. Karatsuba, “Analogi nepolnykh summ Kloostermana i ikh prilozheniya”, Tatra Mt. Math. Publ., 11 (1997), 89–120 | MR | Zbl

[6] A. A. Karatsuba, “Dvoinye summy Kloostermana”, Matem. zametki, 66:5 (1999), 682–687 | DOI | MR | Zbl

[7] M. A. Korolev, “Nepolnye summy Kloostermana i ikh prilozheniya”, Izv. RAN. Ser. matem., 64:6 (2000), 41–64 | DOI | MR | Zbl

[8] M. A. Korolev, “Korotkie summy Kloostermana s vesami”, Matem. zametki, 88:3 (2010), 415–427 | DOI | MR | Zbl

[9] Zh. Burgein, M. Z. Garaev, “Summa mnozhestv, obrazovannykh obratnymi elementami v polyakh prostogo poryadka, i polilineinye summy Kloostermana”, Izv. RAN. Ser. matem., 78:4 (2014), 19–72 | DOI | MR | Zbl

[10] S. V. Konyagin, M. A. Korolev, “O simmetrichnom diofantovom uravnenii s obratnymi velichinami”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Tr. MIAN, 294, MAIK, M., 2016, 76–86 | DOI

[11] P. V. Snurnitsyn, “Ob otsenke srednego znacheniya korotkoi summy Kloostermana”, Uch. zap. Orlovskogo gos. un-ta, 6:2 (2013), 212–215

[12] A. I. Vinogradov, “O chislakh s malymi prostymi delitelyami”, Dokl. AN SSSR, 109:4 (1956), 683–686 | MR | Zbl

[13] M. A. Korolëv, “O metode Karatsuby otsenok summ Kloostermana”, Matem. sb., 207:8 (2016), 117–134 | DOI | MR