In this talk I will discuss our work about two problems on hyperbolic manifolds, the QUE conjecture of Rudnick and Sarnak and the Prime geodesic theorem. For arithmetic manifolds, using triple product formulas and the Kuznetsov trace formula the study of these two problems can be reduced to subconexity estimates for related L-functions. I will describe some of our recent results with a focus on the case of arithmetic 3-manifolds.

• https://aarhusuniversity.zoom.us/j/62837276242