Estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles

Abstract

We find estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles. The geodesic cycles we study are themselves hyperbolic manifolds of lower dimension. The restriction of an automorphic form to such a geodesic cycle can be expanded into eigenfunctions of the Laplacian on the geodesic cycle. We prove exponential decay for the coefficients in this expansion.

23 pages, corrected some typos, updated the references

References in corpus (4)

• Symmetry breaking for representations of rank one orthogonal groups
• Symmetry breaking for representations of rank one orthogonal groups II
• F-method for symmetry breaking operators
• Restriction of some unitary representations of O(1,N) to symmetric subgroups

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• Knapp-Stein type intertwining operators for symmetric pairs
• Symmetry breaking operators for strongly spherical reductive pairs
• Upper bounds for geodesic periods over rank one locally symmetric spaces
• The compact picture of symmetry breaking operators for rank one orthogonal and unitary groups
• Rankin-Selberg periods for spherical principal series
• Upper bounds for geodesic periods over hyperbolic manifolds