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- W3099681538 abstract "In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $mathcal{L}$-operator acting on a space of harmonic cocycles on the Bruhat-Tits tree $mathcal{T}$, which is computable by the methods of Franc and Masdeu described in [FM14]. The main difficulty in computing the $mathcal{L}$-operator is the efficient computation of the $p$-adic Coleman integrals in its definition. To solve this problem, we use overconvergent methods, first developed by Darmon, Greenberg, Pollack and Stevens. In order to make these methods applicable to our setting, we prove a control theorem for $p$-adic automorphic forms of arbitrary even weight. Moreover, we give computational evidence for relations between slopes of $mathcal{L}$-invariants of different levels and weights for $p=2$." @default.
- W3099681538 created "2020-11-23" @default.
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- W3099681538 date "2019-08-21" @default.
- W3099681538 modified "2023-09-24" @default.
- W3099681538 title "A control theorem for p-adic automorphic forms and Teitelbaum’s $$mathcal {L}$$-invariant" @default.
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- W3099681538 doi "https://doi.org/10.1007/s11139-019-00160-1" @default.
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