On démontre que si sont des éléments algébriques de et le groupe engendré par est dense, alors l'opérateur de Hecke défini par ces éléments a un trou spectral.
It is shown that if are algebraic elements in generating a dense subgroup, then the corresponding Hecke operator has a spectral gap.
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@article{CRMATH_2010__348_11-12_609_0, author = {Bourgain, Jean and Gamburd, Alexander}, title = {Spectral gaps in $ \mathit{SU}(d)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {609--611}, publisher = {Elsevier}, volume = {348}, number = {11-12}, year = {2010}, doi = {10.1016/j.crma.2010.04.024}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.04.024/} }
TY - JOUR AU - Bourgain, Jean AU - Gamburd, Alexander TI - Spectral gaps in $ \mathit{SU}(d)$ JO - Comptes Rendus. Mathématique PY - 2010 SP - 609 EP - 611 VL - 348 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.04.024/ DO - 10.1016/j.crma.2010.04.024 LA - en ID - CRMATH_2010__348_11-12_609_0 ER -
%0 Journal Article %A Bourgain, Jean %A Gamburd, Alexander %T Spectral gaps in $ \mathit{SU}(d)$ %J Comptes Rendus. Mathématique %D 2010 %P 609-611 %V 348 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.04.024/ %R 10.1016/j.crma.2010.04.024 %G en %F CRMATH_2010__348_11-12_609_0
Bourgain, Jean; Gamburd, Alexander. Spectral gaps in $ \mathit{SU}(d)$. Comptes Rendus. Mathématique, Tome 348 (2010) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2010.04.024. http://archive.numdam.org/articles/10.1016/j.crma.2010.04.024/
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