[Théorèmes sommes–produits et sommes exponentielles dans les classes de résidus pour module arbitraire]
Dans cette Note, nous généralisons (avec un énoncé approprié) le théorème somme–produit dans
The purpose of this Note is to extend (in the appropriate formulation) the sum–product theorem in
Accepté le :
Publié le :
Jean Bourgain 1
@article{CRMATH_2007__344_6_349_0, author = {Jean Bourgain}, title = {Sum{\textendash}product theorems and exponential sum bounds in residue classes for general modulus}, journal = {Comptes Rendus. Math\'ematique}, pages = {349--352}, publisher = {Elsevier}, volume = {344}, number = {6}, year = {2007}, doi = {10.1016/j.crma.2007.01.019}, language = {en}, }
Jean Bourgain. Sum–product theorems and exponential sum bounds in residue classes for general modulus. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 349-352. doi : 10.1016/j.crma.2007.01.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.019/
[1] Mordell's exponential sum estimate revisited, JAMS, Volume 18 (2005) no. 2, pp. 477-499
[2] Exponential sum estimates over subgroups of
[3] Estimates on exponential sums related to the Diffie–Hellman distributions, GAFA, Volume 15 (2005) no. 1, pp. 1-34
[4] Exponential sum estimates over subgroups and almost subgroups of
[5] J. Bourgain, A. Gamburd, Uniform expansion bounds for Cayley graphs of
[6] Sieving and expanders, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006) no. 3, pp. 155-159
[7] Estimate for the number of sums and products and for exponential sums in fields of prime order, J. London Math. Soc., Volume 73 (2006), pp. 380-398
[8] A sum–product estimate in finite fields and applications, GAFA, Volume 14 (2004), pp. 27-57
[9] Additive Combinatorics, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, 2006
- , Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science (2015), p. 277 | DOI:10.1145/2688073.2688090
- Sums and products along sparse graphs, Israel Journal of Mathematics, Volume 188 (2012) no. 1, p. 353 | DOI:10.1007/s11856-011-0170-x
- Суммы и произведения множеств и оценки рациональных тригонометрических сумм в полях простого порядка, Успехи математических наук, Volume 65 (2010) no. 4, p. 5 | DOI:10.4213/rm9367
- Some effective results for ×a×b, Ergodic Theory and Dynamical Systems, Volume 29 (2009) no. 6, p. 1705 | DOI:10.1017/s0143385708000898
Cité par 4 documents. Sources : Crossref
Commentaires - Politique