Comptes Rendus
Number Theory/Mathematical Analysis
New results on expanders
[Nouveaux résultats sur les expanseurs]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 717-721.

En utilisant d'une approche purement analytique, nous obtenons de nouvelle familles d'expanseurs dans des groupes SL2(p) (p primier) et SU(2). Nos résultats contribuent à des conjectures de A. Lubotzky et P. Sarnak.

Based on purely analytical methods, we exhibit new families of expanders in SL2(p) (p prime) and SU(2), contributing to conjectures of A. Lubotzky and P. Sarnak.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.02.032

Jean Bourgain 1 ; Alex Gamburd 1, 2

1 Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
2 Department of Mathematics, University of California, Santa Cruz, CA 95064, USA
@article{CRMATH_2006__342_10_717_0,
     author = {Jean Bourgain and Alex Gamburd},
     title = {New results on expanders},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {717--721},
     publisher = {Elsevier},
     volume = {342},
     number = {10},
     year = {2006},
     doi = {10.1016/j.crma.2006.02.032},
     language = {en},
}
TY  - JOUR
AU  - Jean Bourgain
AU  - Alex Gamburd
TI  - New results on expanders
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 717
EP  - 721
VL  - 342
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crma.2006.02.032
LA  - en
ID  - CRMATH_2006__342_10_717_0
ER  - 
%0 Journal Article
%A Jean Bourgain
%A Alex Gamburd
%T New results on expanders
%J Comptes Rendus. Mathématique
%D 2006
%P 717-721
%V 342
%N 10
%I Elsevier
%R 10.1016/j.crma.2006.02.032
%G en
%F CRMATH_2006__342_10_717_0
Jean Bourgain; Alex Gamburd. New results on expanders. Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 717-721. doi : 10.1016/j.crma.2006.02.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.032/

[1] J. Bourgain, On the Erdös–Volkmann and Katz–Tao ring conjectures GAFA, 13 (2003) 334–365

[2] J. Bourgain, A. Gamburd, Uniform expansion bounds for Cayley graphs of SL2(Fp), preprint

[3] J. Bourgain, A. Gamburd, On the spectral gap for finitely-generated subgroups of SU(2), preprint

[4] J. Bourgain; N. Katz; T. Tao A sum–product estimate in finite fields and applications, GAFA, Volume 14 (2004), pp. 27-57

[5] J. Bourgain, A. Glibichuk, S. Konyagin, Estimate for the number of sums and product and for exponential sums in fields of prime order, Proc. LMS, in press

[6] J. Conway; C. Radin Quaquaversal tilings and rotations, Invent. Math., Volume 132 (1998), pp. 179-188

[7] C.M. Dawson; M.A. Nielsen The Solovay–Kitaev algorithm, Quantum Inf. Comput., Volume 6 (2006), pp. 81-95

[8] B. Draco; L. Sadun; D. Van Wieren Growth rates in the quaquaversal tiling, Comput. Geom., Volume 23 (2000) no. 3, pp. 419-435

[9] A. Gamburd Spectral gap for infinite index “congruence” subgroups of SL2(Z), Israel J. Math., Volume 127 (2002), pp. 157-200

[10] A. Gamburd; D. Jakobson; P. Sarnak Spectra of elements in the group ring of SU(2), J. Eur. Math. Soc., Volume 1 (1999), pp. 51-85

[11] H. Helfgott, Growth and generation in SL2(Z/pZ), preprint, 2005

[12] N. Katz; T. Tao Some connections between Falconer's distance set conjecture and sets of Furstenberg type, New York J. Math., Volume 7 (2001), pp. 149-187

[13] A. Lubotzky Discrete Groups, Expanding Graphs and Invariant Measures, Progr. Math., vol. 195, Birkhäuser, 1994

[14] A. Lubotzky Cayley graphs: eigenvalues, expanders and random walk (P. Rowbinson, ed.), Surveys in Combinatorics, London Math. Soc. Lecture Note Ser., vol. 218, Cambridge Univ. Press, 1995, pp. 155-189

[15] A. Lubotzky; B. Weiss Groups and expanders (J. Friedaman, ed.), DIMACS Ser. Discrete Math. and Theoret. Comput. Sci., vol. 10, Amer. Math. Soc., 1993, pp. 95-109

[16] P. Sarnak; X. Xue Bounds for multiplicatives of automorphic representations, Duke Math. J., Volume 64 (1991), pp. 207-227

[17] A. Selberg On the estimation of Fourier coefficients of modular forms, Proc. Sympos. Pure Math., vol. VII, Amer. Math. Soc., 1965, pp. 1-15

[18] T. Tao, Non-commutative sum set estimates, preprint

[19] T. Tao, V. Vu, Additive Combinatorics, Cambridge University Press, 2006, in press

  • Alexander Gamburd Arithmetic and dynamics on varieties of Markoff type, International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 3. Sections 1–4, Berlin: European Mathematical Society (EMS), 2023, pp. 1800-1836 | DOI:10.4171/icm2022/191 | Zbl:1551.14103
  • Khodakhast Bibak Additive combinatorics: with a view towards computer science and cryptography – an exposition, Number theory and related fields. In memory of Alf van der Poorten. Based on the proceedings of the international number theory conference, Newcastle, Australia, March 12–16, 2012, New York, NY: Springer, 2013, pp. 99-128 | DOI:10.1007/978-1-4614-6642-0_4 | Zbl:1303.11022
  • Oren Dinai Diameters of Chevalley groups over local rings., Archiv der Mathematik, Volume 99 (2012) no. 5, pp. 417-424 | DOI:10.1007/s00013-012-0451-6 | Zbl:1263.20050
  • Oren Dinai Growth in SL2 over finite fields, Journal of Group Theory, Volume 14 (2011) no. 2 | DOI:10.1515/jgt.2010.056
  • Alexander Lubotzky Finite simple groups of Lie type as expanders., Journal of the European Mathematical Society (JEMS), Volume 13 (2011) no. 5, pp. 1331-1341 | DOI:10.4171/jems/282 | Zbl:1257.20016
  • Мубарис Зафар оглы Гараев; Mubaris Zafar ogly Garaev 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
  • Aram W. Harrow; Richard A. Low Efficient Quantum Tensor Product Expanders and k-Designs, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Volume 5687 (2009), p. 548 | DOI:10.1007/978-3-642-03685-9_41
  • Iddo Samet Rigid actions of amenable groups, Israel Journal of Mathematics, Volume 173 (2009), pp. 61-90 | DOI:10.1007/s11856-009-0083-0 | Zbl:1187.43003
  • A. Wigderson, 21st Annual IEEE Conference on Computational Complexity (CCC'06) (2006), p. 111 | DOI:10.1109/ccc.2006.9

Cité par 9 documents. Sources : Crossref, zbMATH

Commentaires - Politique


Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !


Publier un nouveau commentaire:

Publier une nouvelle réponse: