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 $\mathbb Q(\sqrt {D})$.References
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Bibliographic Information
- Bingrong Huang
- Affiliation: Data Science Institute and School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
- MR Author ID: 1088033
- ORCID: 0000-0002-8987-0015
- Email: brhuang@sdu.edu.cn
- Stephen Lester
- Affiliation: School of Mathematical Sciences, Queen Mary University of London, E1 4NS London, United Kingdom
- Address at time of publication: Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom
- MR Author ID: 988132
- Email: s.lester@qmul.ac.uk, steve.lester@kcl.ac.uk
- Received by editor(s): December 21, 2021
- Received by editor(s) in revised form: July 13, 2022
- Published electronically: October 13, 2022
- Additional Notes: The first author was partially supported by the National Key R&D Program of China 2021YFA1000700 and NSFC 12001314 and 12031008. The second author was partially supported by EPSRC Standard Grant EP/T028343/1.
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 643-695
- MSC (2020): Primary 11F12, 11F72; Secondary 11M41, 58J51
- DOI: https://doi.org/10.1090/tran/8780
- MathSciNet review: 4510120