Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative functoriality and functional equations via trace formulas   Langlands' functoriality principle predicts deep relations between the local
and automorphic spectra of different reductive groups. This has been
generalized by the relative Langlands program to include spherical varieties,
among which reductive groups are special cases. In the philosophy of Langlands'
"beyond endoscopy" program, these relations should be expressed as comparisons
between different trace formulas, with the insertion of appropriate
$L$-functions. The insertion of $L$-functions calls for one more goal to be
achieved: the study of their functional equations via trace formulas.
  The goal of this article is to demonstrate this program through examples,
indicating a local-to-global approach as in the project of endoscopy. Here,
scalar transfer factors are replaced by "transfer operators" or "Hankel
transforms" which are nice enough (typically, expressible in terms of usual
Fourier transforms) that they can be used, in principle, to prove global
comparisons (in the form of Poisson summation formulas). Some of these examples
have already appeared in the literature; for others, the proofs will appear
elsewhere.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph