Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonvanishing modulo $\ell$ of Fourier coefficients of Jacobi forms   Let $\phi = \sum_{r^{2} \leq 4mn}c(n,r)q^{n}\zeta^{r}$ be a Jacobi form of
weight $k$ (with $k > 2$ if $\phi$ is not a cusp form) and index $m$ with
integral algebraic coefficients which is an eigenfunction of all Hecke
operators $T_{p}, (p,m) = 1,$ and which has at least one nonvanishing
coefficient $c(n,r)$ with $r$ prime to $m$. We prove that for almost all primes
$\ell$ there are infinitely many fundamental discriminants $D = r^{2}-4mn < 0$
prime to $m$ with $\nu_{\ell}(c(n,r)) = 0$, where $\nu_{\ell}$ denotes a
continuation of the $\ell$-adic valuation on $\mathbb{Q}$ to an algebraic
closure. As applications we show indivisibility results for special values of
Dirichlet $L$-series and for the central critical values of twisted
$L$-functions of even weight newforms.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org