Bounds for the periods of eigenfunctions on arithmetic hyperbolic 3-manifolds over surfaces

Abstract Let $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> be a Hecke–Maass form on a compact congruence arithmetic hyperbolic 3-manifold X , and let Y be a totally geodesic surface in X that is not necessarily closed. We obtain a power saving result over the local bound for the period of $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> along Y , by applying the method of arithmetic amplification developed by Iwaniec and Sarnak.