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Equidistribution of cusp forms on \(\text{PSL}_ 2({\mathbb{Z}})\setminus \text{PSL}_ 2({\mathbb{R}})\). (English) Zbl 0868.43011
Summary: We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on \(\text{PSL}_2({\mathbb{Z}})\setminus \text{PSL}_2 ({\mathbb{R}})\). This generalizes a recent result of W. Luo and P. Sarnak [Publ. Math., Inst. Hautes Étud. Sci. 81, 207-237 (1995; Zbl 0852.11024)] who prove equidistribution on \(\text{PSL}_2({\mathbb{Z}})\setminus {\mathbb{H}}\).

MSC:
43A85 Harmonic analysis on homogeneous spaces
11F11 Holomorphic modular forms of integral weight
81Q50 Quantum chaos
58C40 Spectral theory; eigenvalue problems on manifolds
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