Mass equidistribution on the torus in the depth aspect
It is known that the quantum unique ergodicity (QUE) propery in the arithmetic setting is a special case of the conjecture by \textit{Z. Rudnick} and \textit{P. Sarnak} [Commun. Math. Phys. 161, No. 1, 195--213 (1994; Zbl 0836.58043)] regarding the asymptotic behavior of the mass measure associated to a normalized holomorphic modular form or Maass form. The aim of the present paper is to study the equidistribution of the restriction of the mass of automorphic newforms to a nonsplit torus in the depth aspect. To this direction the author manages to prove a better result than the already known results on the similar problem in the eigenvalue aspect by using a relatively elementary method which makes use of the known effective QUE result in the depth aspect.
scientific article; zbMATH DE number 7224495
scientific article