We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on Γ0(D)\H in the large eigenvalue limit, for certain fixed D. As predicted in the physics literature, the resulting quadratic form is related to the classical variance of the geodesic flow on Γ0(D)\H, but also includes factors that are sensitive to underlying arithmetic of the number field Q(√D).
- Quantum variance
- dihedral Maass form
- generalized Ramanujan conjecture
- generalized Riemann hypothesis
- quantum covariance