Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On special zeros of $p$-adic $L$-functions of Hilbert modular forms   Let $E$ be a modular elliptic curve over a totally real number field $F$. We
prove the weak exceptional zero conjecture which links a (higher) derivative of
the $p$-adic $L$-function attached to $E$ to certain $p$-adic periods attached
to the corresponding Hilbert modular form at the places above $p$ where $E$ has
split multiplicative reduction. Under some mild restrictions on $p$ and the
conductor of $E$ we deduce the exceptional zero conjecture in the strong form
(i.e.\ where the automorphic $p$-adic periods are replaced by the
$\cL$-invariants of $E$ defined in terms of Tate periods) from a special case
proved earlier by Mok. Crucial for our method is a new construction of the
$p$-adic $L$-function of $E$ in terms of local data.

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The categories of this paper are: q-fin
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat