Israel Journal of Mathematics

, Volume 88, Issue 1, pp 31-72

First online:

Betti numbers of congruence groups

  • Peter SarnakAffiliated withDepartment of Mathematics, Princeton University Email author 
  • , Scot AdamsAffiliated withDepartment of Mathematics, University of Minnesota
  • , Ze'ev RudnickAffiliated withDepartment of Mathematics, Princeton University

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It is shown that, for certain congruence families of Galois coverings of a manifold, the individual Betti numbers are polynomial periodic functions of the level. Similar results are proved for the dimensions of other spaces of automorphic forms.