Upper bounds for geodesic periods over rank one locally symmetric spaces

Jan Frahm*, Feng Su

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1065-1077
Number of pages13
JournalForum Mathematicum
Issue number5
Publication statusPublished - 1 Sept 2018
Externally publishedYes


  • Locally symmetric spaces
  • automorphic forms
  • geodesic periods
  • reductive Lie groups
  • totally geodesic cycles
  • unitary representations

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