Quantum Variance for Eisenstein Series
Copyright policy )Quantum Variance for Eisenstein Series
Abstract In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on $\operatorname{PSL}_2(\mathbb{Z})\backslash \mathbb{H}$. The resulting quadratic form is compared with the classical variance and the quantum variance for cusp forms. They coincide after inserting certain subtle arithmetic factors, including the central values of certain L-functions.
- Shandong Women’s University China (People's Republic of)
- Tel Aviv University Israel
Mathematics - Analysis of PDEs, Mathematics - Number Theory, FOS: Mathematics, FOS: Physical sciences, Number Theory (math.NT), Mathematical Physics (math-ph), Mathematical Physics, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, Mathematics - Number Theory, FOS: Mathematics, FOS: Physical sciences, Number Theory (math.NT), Mathematical Physics (math-ph), Mathematical Physics, Analysis of PDEs (math.AP)
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