Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $p$-adic $L$-functions of Hilbert cusp forms and the trivial zero
  conjecture   We prove a strong form of the trivial zero conjecture at the central point
for the $p$-adic $L$-function of a non-critically refined self-dual
cohomological cuspidal automorphic representation of $\mathrm{GL}_2$ over a
totally real field, which is Iwahori spherical at places above $p$. In the case
of a simple zero we adapt the approach of Greenberg and Stevens, based on the
functional equation for the $p$-adic $L$-function of a nearly finite slope
family and on improved $p$-adic $L$-functions that we construct using
automorphic symbols and overconvergent cohomology. For higher order zeros we
develop a conceptually new approach studying the variation of the root number
in partial families and establishing the vanishing of many Taylor coefficients
of the $p$-adic $L$-function of the family.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: cs