Soit (p premier) d'ordre multiplicatif t>pδ, on obtient des bornes non-triviales sur les sommes exponentielles
Given (p prime) of multiplicative order t>pδ, we obtain nontrivial bounds on exponential sums
Accepté le :
Publié le :
Jean Bourgain 1
@article{CRMATH_2004__338_11_825_0, author = {Jean Bourgain}, title = {New bounds on exponential sums related to the {Diffie{\textendash}Hellman} distributions}, journal = {Comptes Rendus. Math\'ematique}, pages = {825--830}, publisher = {Elsevier}, volume = {338}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.03.027}, language = {en}, }
Jean Bourgain. New bounds on exponential sums related to the Diffie–Hellman distributions. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 825-830. doi : 10.1016/j.crma.2004.03.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.027/
[1] Exponential sums over Mersenne numbers, Compositio Math., Volume 140 (2004) no. 1, pp. 15-30
[2] On the Erdös–Volkmann and Katz–Tao ring conjectures, Geom. Funct. Anal., Volume 13 (2003) no. 2, pp. 334-365
[3] J. Bourgain, N. Katz, T. Tao, A sum-product theorem in finite fields and applications, Geom. Funct. Anal., in press
[4] Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 337 (2003) no. 2, pp. 75-80
[5] On the statistical properties of Diffie–Hellman distributions, Israel J. Math. A, Volume 120 (2000), pp. 23-46
[6] Some doubly exponential sums over , Acta Arith., Volume 105 (2002) no. 4, pp. 349-370
[7] S. Konyagin, Private communications
[8] Prime divisors of sparse integers, Period. Math. Hungar., Volume 96 (2003) no. N2, pp. 215-222
Cité par Sources :
Commentaires - Politique