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Expansion in SL d (Z/q Z), q arbitrary

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Let S be a fixed finite symmetric subset of SL d (Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of π q (G) with respect to the generating set π q (S) form a family of expanders, where π q is the projection map Z→Z/q Z.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Jean Bourgain

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Péter P. Varjú

  3. Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, University of Szeged, Szeged, Hungary

    Péter P. Varjú

Authors
  1. Jean Bourgain
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  2. Péter P. Varjú
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Corresponding author

Correspondence to Jean Bourgain.

Additional information

J. Bourgain was supported by the NSF grants DMS-0808042 and DMS-0835373.

P.P. Varjú was supported by the Fulbright Science and Technology Award 15073240.

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Bourgain, J., Varjú, P.P. Expansion in SL d (Z/q Z), q arbitrary. Invent. math. 188, 151–173 (2012). https://doi.org/10.1007/s00222-011-0345-4

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