%0 Journal Article
%T Expansion in $SL_d(O_K/I)$, $I$ square-free
%A P¨¦ter P. Varj¨˛
%J Mathematics
%D 2010
%I arXiv
%R 10.4171/JEMS/302
%X Let S be a fixed symmetric finite subset of SL_d(O_K) that generates a Zariski dense subgroup of SL_d(O_K) when we consider it as an algebraic group over Q by restriction of scalars. We prove that the Cayley graphs of SL_d(O_K/I) with respect to the projections of S is an expander family if I ranges over square-free ideals of O_K if d=2 and K is an arbitrary numberfield, or if d=3 and K=Q.
%U http://arxiv.org/abs/1001.3664v1