Geodesic
Expansion in $SL_d(\mathcal{O}_K/I)$, $I$ square-free
Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 273-305.

Voir la notice de l'article provenant de la source EMS Press

Let S be a fixed symmetric finite subset of SLd​(OK​) that generates a Zariski dense subgroup of SLd​(OK​) when we consider it as an algebraic group over Q by restriction of scalars. We prove that the Cayley graphs of SLd​(OK​/I) with respect to the projections of S is an expander family if I ranges over square-free ideals of OK​ if d=2 and K is an arbitrary numberfield, or if d=3 and K=Q.
DOI : 10.4171/jems/302
Classification : 60-XX, 05-XX, 20-XX, 00-XX
Keywords: Expanders, property tau, Cayley graphs, random walks on groups, affine sieve 
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     author = {P\'eter P. Varj\'u},
     title = {Expansion in $SL_d(\mathcal{O}_K/I)$, $I$ square-free},
     journal = {Journal of the European Mathematical Society},
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     volume = {14},
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     doi = {10.4171/jems/302},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/302/}
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Péter P. Varjú. Expansion in $SL_d(\mathcal{O}_K/I)$, $I$ square-free. Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 273-305. doi : 10.4171/jems/302. http://geodesic.mathdoc.fr/articles/10.4171/jems/302/

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