Speaker: Adel Betina (UPC)

The p-stabilization of certain Eisenstein weight one forms are cuspidal-overconvergent forms, and they belong to the cuspidal locus of the p-adic eigencurve.

I will explain during this talk when this situation happens, and I will explain also the connection with the trivial zeros of the Leopoldt-Kubota p-adic L-function. Finally, I will state my last result with Mladen Dimitrov about the local structure of the eigencurve at these points and the possible generalizations for the Hilbert case.

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