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arXiv · 2402.18218

Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds

Zvi Shem-Tov·Lior Silberman
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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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Zvi Shem-Tov, Lior Silberman. 2024-02-28. Homogeneity of arithmetic quantum limits for hyperbolic $4$-manifolds. https://arxiv.org/abs/2402.18218

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