Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eisenstein series and the cubic moment for PGL(2)   Following a strategy suggested by Michel--Venkatesh, we study the cubic
moment of automorphic $L$-functions on $\operatorname{PGL}_2$ using regularized
diagonal periods of products of Eisenstein series. Our main innovation is to
produce vectors whose integral transforms achieve arbitrarily weighted moments.
Applications include general Motohashi-type identities and Weyl-type subconvex
bounds for some families of $L$-functions, extending some results of
Conrey--Iwaniec and Petrow--Young to the number field setting. We deduce
improved estimates for representation numbers of ternary quadratic forms over
number fields and for the prime geodesic theorem on arithmetic hyperbolic
$3$-folds.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys