Planck-scale mass equidistribution conjecture for dihedral Maaß newforms

Let $g\to\frac12+it_g$ be a sequence of newforms in $\mathcal{B}_0^{\ast}(q,\chi)$, and let $R$ denote the radius of a hyperbolic ball. The volume-level shrinking-ball equidistribution statement is denoted by

$$. **Planck-scale mass equidistribution conjecture.** Suppose that$$

R\gg t_g^{-\delta},\qquad 0<\delta<1.

$$Then$$

holds as $t_g$ tends to infinity along any subsequence of newforms $g\in\mathcal{B}_0^{\ast}(q,\chi)$. This is a small-scale form of quantum unique ergodicity for almost every shrinking ball above the Planck scale. The corresponding pointwise statement is known only in more restricted ranges or under additional hypotheses, while the variance formulation has been established for $q=1$ under the generalized Lindelöf hypothesis and for Eisenstein series unconditionally.