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arXiv · 2007.02055

Quantum variance for dihedral Maass forms

Bingrong Huang·Stephen Lester
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Abstract

We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on $\Gamma_0(D) \backslash \mathbb H$ in the large eigenvalue limit, for certain fixed $D$. As predicted in the physics literature, the resulting quadratic form is related to the classical variance of the geodesic flow on $\Gamma_0(D) \backslash \mathbb H$, but also includes factors that are sensitive to underlying arithmetic of the number field $\mathbb Q(\sqrt{D})$.

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Bingrong Huang, Stephen Lester. 2020-07-04. Quantum variance for dihedral Maass forms. https://arxiv.org/abs/2007.02055

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