The quantum unique ergodicity conjecture for thin sets

Abstract

We consider some analogs of the quantum unique ergodicity conjecture for geodesics, horocycles, or ``shrinking'' families of sets. In particular, we prove the analog of the QUE conjecture for Eisenstein series restricted to the infinite geodesic connecting 0 and infinity inside the modular surface.

53 pages

References in corpus (6)

• Distribution of mass of holomorphic cusp forms
• Nodal domains of Maass forms I
• Rankin Triple Products and Quantum Chaos
• Subconvexity and equidistribution of Heegner points in the level aspect
• Upper bounds on L-functions at the edge of the critical strip
• Quantum ergodicity for restrictions to hypersurfaces

Cited by in corpus (27)

• Explicit calculations with Eisenstein series
• Planck-scale mass equidistribution of toral Laplace eigenfunctions
• Equidistribution in Shrinking Sets and L^4-Norm Bounds for Automorphic Forms
• Small scale equidistribution of eigenfunctions on the torus
• A note on the sup norm of Eisenstein series
• $L^p$ norms, nodal sets, and quantum ergodicity
• Small scale equidistribution of random eigenbases
• On the Random Wave Conjecture for Dihedral Maaß Forms
• Applications of small scale quantum ergodicity in nodal sets
• Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions
• CLT for Planck scale mass distribution of toral Laplace eigenfunctions
• Equidistribution of Eisenstein series on geodesic segments
• Test vectors for Waldspurger's period integral and application to the mass equidistribution on nonsplit torus
• Quantum Unique Ergodicity for Eisenstein Series in the Level Aspect
• Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-Maaß Cusp Forms on ${\mathrm{SL}}_2(\mathbb{Z})\backslash {\mathrm{SL}}_2(\mathbb{R})$
• Correction to: Equidistribution of Eisenstein Series in the Level Aspect
• New variants of arithmetic quantum ergodicity
• Small scale quantum ergodicity in cat maps. I
• Sign changes of the Eisenstein series on the critical line
• Mass distribution for toral eigenfunctions via Bourgain's de-randomisation
• Small scale equidistribution for a point scatterer on the torus
• Extreme values of geodesic periods on arithmetic hyperbolic surfaces
• Quantum ergodicity for shrinking balls in arithmetic hyperbolic manifolds
• On the $L^2$ restriction norm of large level
• Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic
• Quantum Limits of Eisenstein Series in H^3
• Distribution of the nodal sets of eigenfunctions on analytic manifolds