Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pullbacks of Siegel Eisenstein Series and Weighted Averages of Critical
  $L$-values   In this paper we obtain a weighted average formula for special values of
$L$-functions attached to normalized elliptic modular forms of weight $k$ and
full level. These results are obtained by studying the pullback of a Siegel
Eisenstein series and working out an explicit spectral decomposition.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an