Geodesic
Group Theory/Number Theory
Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order
[Estimes sommes–produits et sur les sommes exponentielles associées à des sous-groupes d'un corps d'ordre premier]
Présenté par : Jean Bourgain
Bourgain, Jean1, 2 ; Konyagin, S.V.3
1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
2 Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
3 Department of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia
Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 75-80

Voir la notice de l'article provenant de la source Numdam

Our first result is a ‘sum–product’ theorem for subsets A of the finite field 𝔽 p , p prime, providing a lower bound on max(|A+A|,|A·A|). As corollary, the second and main result provides new bounds on exponential sums associated to subgroups of the multiplicative group 𝔽 p * .

Notre premier résultat est un théorème « sommes–produits » pour des sous-ensembles A d'un corps fini 𝔽 p , p un nombre premier, donnant une minoration du max(|A+A|,|A·A|). Comme corollaire et résultat principal, on en déduit de nouvelles bornes sur les sommes exponentielles associées à des sous-groupes du groupe multiplicatif 𝔽 p * .

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00281-4

Bourgain, Jean 1, 2 ; Konyagin, S.V. 3

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
2 Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
3 Department of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia 
@article{CRMATH_2003__337_2_75_0,
     author = {Bourgain, Jean and Konyagin, S.V.},
     title = {Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {75--80},
     publisher = {Elsevier},
     volume = {337},
     number = {2},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00281-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(03)00281-4/}
}
TY  - JOUR
AU  - Bourgain, Jean
AU  - Konyagin, S.V.
TI  - Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 75
EP  - 80
VL  - 337
IS  - 2
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(03)00281-4/
DO  - 10.1016/S1631-073X(03)00281-4
LA  - en
ID  - CRMATH_2003__337_2_75_0
ER  - 
%0 Journal Article
%A Bourgain, Jean
%A Konyagin, S.V.
%T Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order
%J Comptes Rendus. Mathématique
%D 2003
%P 75-80
%V 337
%N 2
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(03)00281-4/
%R 10.1016/S1631-073X(03)00281-4
%G en
%F CRMATH_2003__337_2_75_0
Bourgain, Jean; Konyagin, S.V. Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order. Comptes Rendus. Mathématique, Tome 337 (2003) no. 2, pp. 75-80. doi: 10.1016/S1631-073X(03)00281-4

Cité par Sources :