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Hu, Yueke

Mass equidistribution on the torus in the depth aspect. (English) Zbl 1476.58032

Algebra Number Theory 14, No. 4, 927-946 (2020).
It is known that the quantum unique ergodicity (QUE) propery in the arithmetic setting is a special case of the conjecture by Z. Rudnick and 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.
Reviewer: Chryssoula Ganatsiou (Larissa)

MSC:

58J51 Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity
37A30 Ergodic theorems, spectral theory, Markov operators
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
22E50 Representations of Lie and linear algebraic groups over local fields
37A46 Relations between ergodic theory and harmonic analysis

Keywords:

equidistribution in the depth aspect; restriction of mass measure to torus; quantum unique ergodicity (QUE) propery

Citations:

Zbl 0836.58043
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\textit{Y. Hu}, Algebra Number Theory 14, No. 4, 927--946 (2020; Zbl 1476.58032)
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