1 Correction to: Mathematische Zeitschrift https://doi.org/10.1007/s00209-020-02665-8
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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.
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Nelson, P.D. Correction to: The spectral decomposition of \(|\theta |^2\). Math. Z. 299, 1197 (2021). https://doi.org/10.1007/s00209-020-02668-5
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DOI: https://doi.org/10.1007/s00209-020-02668-5