Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds
Number Theory
2024-04-04 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We work toward the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke--Maass forms on hyperbolic -manifolds. We show that limits of such forms can only scar on totally geodesic -submanifolds, and in fact that all ergodic components of the microlocal lift other than the uniform measure arise from the uniform measures on these submanifolds.
Cite
@article{arxiv.2402.18218,
title = {Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds},
author = {Zvi Shem-Tov and Lior Silberman},
journal= {arXiv preprint arXiv:2402.18218},
year = {2024}
}
Comments
22 pages; minor revision including additional reference