Mass equidistribution on the torus in the depth aspect
type: Item
instance of: scholarly article
title: Mass equidistribution on the torus in the depth aspect
zbMATH Open document ID: 1476.58032
author: Yueke Hu
published in: Algebra \& Number Theory
publication date: 2020-07-24T00:00:00Z
full work available at URL: http://hdl.handle.net/21.11116/0000-0007-E29F-7
review text: 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.
Mathematics Subject Classification ID: 58J51
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 37A46
zbMATH DE Number: 7224495
zbMATH Keywords: equidistribution in the depth aspect
zbMATH Keywords: restriction of mass measure to torus
zbMATH Keywords: quantum unique ergodicity (QUE) propery
reviewed by: Chryssoula Ganatsiou
MaRDI profile type: Publication
OpenAlex ID: W3036557946
cites work: On the Ramanujan conjecture over number fields
cites work: The second moment of twisted modular \(L\)-functions
cites work: Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
cites work: On some results of Atkin and Lehner
cites work: Quantum ergodic restriction for Cauchy data: interior QUE and restricted QUE
cites work: On the order of vanishing of newforms at cusps
cites work: Quantum ergodicity for restrictions to hypersurfaces
cites work: Nodal domains of Maass forms. I
cites work: Mass equidistribution for Hecke eigenforms
cites work: Triple product formula and the subconvexity bound of Triple product L-function in level aspect
cites work: Triple Product Formula and Mass Equidistribution on Modular Curves of Level N
cites work: Trilinear forms and the central values of triple product \(L\)-functions
cites work: Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph
cites work: Mass equidistribution for automorphic forms of cohomological type on 𝐺𝐿₂
cites work: Geodesic restrictions of arithmetic eigenfunctions
cites work: The subconvexity problem for \(\mathrm{GL}_2\)
cites work: Equidistribution of cusp forms in the level aspect
cites work: Subconvex equidistribution of cusp forms: reduction to Eisenstein observables
cites work: Bounds for Rankin-Selberg integrals and quantum unique ergodicity for powerful levels
cites work: The behaviour of eigenstates of arithmetic hyperbolic manifolds
cites work: Quantum unique ergodicity for \(\text{SL}_2(\mathbb Z)\setminus \mathbb H\)
cites work: Quantum ergodic restriction theorems: manifolds without boundary
cites work: Sparse equidistribution problems, period bounds and subconvexity
cites work: Q3682555
cites work: Equidistribution of Eisenstein series on geodesic segments
DOI: 10.2140/ANT.2020.14.927
description: scientific article; zbMATH DE number 7224495