1 Correction to: Mathematische Zeitschrift https://doi.org/10.1007/s00209-020-02665-8

In the original publication, the publisher added irrelevant content to the Abstract section by mistake. The correct Abstract section is given here.

Abstract

Let \(\theta \) be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for \(\langle |\theta |^2, \varphi \rangle \) as \(\varphi \) traverses a sequence of Hecke-translates of a nice enough fixed function. The subtlety is that typically \(|\theta |^2 \notin L^2\). Applications to the subconvexity, quantum variance and 4-norm problems are indicated.

The original article has been corrected.