Homogeneity of arithmetic quantum limits for hyperbolic 4-manifolds

2024/02/28 by Shem-Tov, Zvi, Silberman, Lior
#11F41 #37A45 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.18218

Abstract

We work toward the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke--Maass forms on hyperbolic 4-manifolds. We show that limits of such forms can only scar on totally geodesic 3-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.

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