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- W2951636250 abstract "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." @default.
- W2951636250 created "2019-06-27" @default.
- W2951636250 creator A5044516628 @default.
- W2951636250 date "2012-07-10" @default.
- W2951636250 modified "2023-09-28" @default.
- W2951636250 title "On special zeros of $p$-adic $L$-functions of Hilbert modular forms" @default.
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