QUANTUM VARIANCE FOR DIHEDRAL MAASS FORMS

Bingrong Huang; Stephen Lester

doi:10.1090/tran/8780

QUANTUM VARIANCE FOR DIHEDRAL MAASS FORMS

Bingrong Huang, Stephen Lester

Research output: Contribution to journal › Article › peer-review

Abstract

We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on Γ0(D)\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 Γ0(D)\H, but also includes factors that are sensitive to underlying arithmetic of the number field Q(√D).

Original language	English
Pages (from-to)	643-695
Number of pages	53
Journal	Transactions of the American Mathematical Society
Volume	376
Issue number	1
DOIs	https://doi.org/10.1090/tran/8780
State	Published - 1 Jan 2023
Externally published	Yes

Keywords

Lfunction
Quantum variance
dihedral Maass form
generalized Ramanujan conjecture
generalized Riemann hypothesis
quantum covariance

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10.1090/tran/8780

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abstract = "We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on Γ0(D)\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 Γ0(D)\H, but also includes factors that are sensitive to underlying arithmetic of the number field Q(√D).",

keywords = "Lfunction, Quantum variance, dihedral Maass form, generalized Ramanujan conjecture, generalized Riemann hypothesis, quantum covariance",

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KW - dihedral Maass form

KW - generalized Ramanujan conjecture

KW - generalized Riemann hypothesis

KW - quantum covariance

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QUANTUM VARIANCE FOR DIHEDRAL MAASS FORMS

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