Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruence primes for automorphic forms on unitary groups and
  applications to the arithmetic of Ikeda lifts   In this paper we provide a sufficient condition for a prime to be a
congruence prime for an automorphic form $f$ on the unitary group $U(n,n)(A_F)$
for a large class of totally real fields $F$ via a divisibility of a special
value of the standard $L$-function associated to $f$. We also study $\ell$-adic
properties of the Fourier coefficients of an Ikeda lift $I_{\phi}$ (of an
elliptic modular form $\phi$) on $U(n,n)(A_{\mathbf{Q}})$ proving that they are
$\ell$-adic integers which do not all vanish modulo $\ell$. Finally we combine
these results to show that the condition of $\ell$ being a congruence prime for
$I_{\phi}$ is controlled by the $\ell$-divisibility of a product of special
values of the symmetric square $L$-function of $\phi$. We close the paper by
computing an example when our main theorem applies.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat