[Estimes sommes–produits et sur les sommes exponentielles associées à des sous-groupes d'un corps d'ordre premier]
Notre premier résultat est un théorème « sommes–produits » pour des sous-ensembles A d'un corps fini , 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 .
Our first result is a ‘sum–product’ theorem for subsets A of the finite field , 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 .
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@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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. http://www.numdam.org/articles/10.1016/S1631-073X(03)00281-4/
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