Quantum variance for Eisenstein Series

Abstract

In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on ${\mathrm{PSL}}_2(\mathbb{Z})\backslash \mathbb{H}$. 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.

19 pages. Comments are welcome