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MR2746949 (2012i:11008) 11B30 (11B05 11L07 11P55)
Bourgain, Jean; Kontorovich, Alex On representations of integers in thin subgroups of ${\rm SL}\sb 2(\Bbb Z)$. Geom. Funct. Anal. 20 (2010), no. 5, 1144–1174.
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