Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spectral decomposition of $|\theta|^2$   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.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat