Upper bounds for geodesic periods over rank one locally symmetric spaces

  • 1 Department Mathematik, Friedrich-Alexander-Universität Erlangen–Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany
  • 2 Institute of Mathematics, Chinese Academy of Sciences, AMSS, Beijing, P. R. China
Jan FrahmORCID iD: http://orcid.org/0000-0003-4174-5933 and Feng SuORCID iD: http://orcid.org/0000-0002-4867-5897

Abstract

We prove upper bounds for geodesic periods of automorphic forms over general rank one locally symmetric spaces. Such periods are integrals of automorphic forms restricted to special totally geodesic cycles of the ambient manifold and twisted with automorphic forms on the cycles. The upper bounds are in terms of the Laplace eigenvalues of the two automorphic forms, and they generalize previous results for real hyperbolic manifolds to the context of all rank one locally symmetric spaces.

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