Quantum variance for dihedral Maass forms

Huang, Bingrong; Lester, Stephen

doi:10.1090/tran/8780

Quantum variance for dihedral Maass forms
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by Bingrong Huang and Stephen Lester;

Trans. Amer. Math. Soc. 376 (2023), 643-695

DOI: https://doi.org/10.1090/tran/8780

Published electronically: October 13, 2022

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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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Quantum variance for dihedral Maass forms
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Abstract: