We establish a Szemerédi–Trotter type result for hyperbolas in .
Nous démontrons une version du théorème de Szemerédi–Trotter pour des familles dʼhyperboles dans .
Accepted:
Published online:
Jean Bourgain 1
@article{CRMATH_2012__350_17-18_793_0, author = {Jean Bourgain}, title = {A modular {Szemer\'edi{\textendash}Trotter} theorem for hyperbolas}, journal = {Comptes Rendus. Math\'ematique}, pages = {793--796}, publisher = {Elsevier}, volume = {350}, number = {17-18}, year = {2012}, doi = {10.1016/j.crma.2012.09.011}, language = {en}, }
Jean Bourgain. A modular Szemerédi–Trotter theorem for hyperbolas. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 793-796. doi : 10.1016/j.crma.2012.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.09.011/
[1] More on the sum-product phenomenon in prime fields and its applications, Int. J. Number Theory, Volume 1 (2005) no. 1, pp. 1-32
[2] Uniform expansion bounds for Cayley graphs of , Annals of Math., Volume 167 (2008), pp. 625-642
[3] A sum-product estimate in finite fields and applications, GAFA, Volume 14 (2004), pp. 27-57
[4] Growth and generation in , Annals of Math., Volume 167 (2008) no. 2, pp. 601-623
[5] An explicit incidence theorem in | arXiv
[6] Bounds for multiplicities of automorphic representations, Duke Math. J., Volume 64 (1991), pp. 207-227
Cited by Sources:
☆ The research was partially supported by NSF grants DMS-0808042 and DMS-0835373.
Comments - Policy