Geodesic
Incomplete Kloosterman sums and their applications
Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1129-1152.

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

We obtain a non-trivial estimate for the upper bound of the absolute value of incomplete Kloosterman sums in which the number of terms is much less than the modulus. 
@article{IM2_2000_64_6_a1,
     author = {M. A. Korolev},
     title = {Incomplete {Kloosterman} sums and their applications},
     journal = {Izvestiya. Mathematics },
     pages = {1129--1152},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a1/}
}
TY  - JOUR
AU  - M. A. Korolev
TI  - Incomplete Kloosterman sums and their applications
JO  - Izvestiya. Mathematics 
PY  - 2000
SP  - 1129
EP  - 1152
VL  - 64
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a1/
LA  - en
ID  - IM2_2000_64_6_a1
ER  - 
%0 Journal Article
%A M. A. Korolev
%T Incomplete Kloosterman sums and their applications
%J Izvestiya. Mathematics 
%D 2000
%P 1129-1152
%V 64
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a1/
%G en
%F IM2_2000_64_6_a1
M. A. Korolev. Incomplete Kloosterman sums and their applications. Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1129-1152. http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a1/

[1] Kloosterman H. D., “On the representation of numbers in the form $ax^2+by^2+cz^2+dt^2$”, Acta Math., 49 (1926), 407–464 | DOI | MR

[2] Salie H., “Über die Kloostermanschen Summen $S(u,v,q)$”, Math. Z., 34 (1931), 91–109 | DOI | MR

[3] Weil A., “On some exponential sums”, Proc. Nat. Acad. Sci. USA, 34 (1948), 204–207 | DOI | MR | Zbl

[4] Carlitz L., Uchiyama S., “Bounds for exponential sums”, Duke Math. J., 24 (1957), 37–41 | DOI | MR | Zbl

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

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

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

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

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

[10] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1967 | MR

[11] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, 2-e izd., Nauka, M., 1983 | MR