Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adelic Integrable Systems   Incorporating the zonal spherical function (zsf) problems on real and
$p$-adic hyperbolic planes into a Zakharov-Shabat integrable system setting, we
find a wide class of integrable evolutions which respect the number-theoretic
properties of the zsf problem. This means that at {\it all} times these real
and $p$-adic systems can be unified into an adelic system with an $S$-matrix
which involves (Dirichlet, Langlands, Shimura...) L-functions.

36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex