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- W2757100850 abstract "In the first part of the paper, we show that any cohomological Hilbertmodular cusp form which is non-critical and of nearly finite slope at $p$, inthe sense that the local representation is not supercuspidal at any place above$p$, belongs to a unique $p$-adic family of maximal dimension. Further, usingautomorphic symbols for Hilbert modular varieties, we construct a functorialmap sending a finite slope overconvergent cohomology class to a distributionover the Galois group of the maximal abelian $p$-ramified extension. Theseevaluation maps yield, in a unified fashion, both $p$-adic $L$-functions fornearly finite slope families and their improved counterparts. In the second part of the paper we prove the exceptional zero conjecture atthe central point for the Greenberg-Benois $p$-adic $mathscr{L}$-invariant inthe case of Hilbert modular forms which are in addition Iwahori spherical atplaces above $p$ and have trivial central character. In the case of a multipleexceptional zero we go beyond the Greenberg-Stevens method and use theinterplay between partial finite slope families and partially improved $p$-adic$L$-functions to establish the vanishing of many Taylor coefficients of the$p$-adic $L$-function of the family." @default.
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- W2757100850 date "2017-09-23" @default.
- W2757100850 modified "2023-09-27" @default.
- W2757100850 title "$p$-adic $L$-functions for Nearly Finite Slope Hilbert Modular Forms and Exceptional Zero Conjectures" @default.
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