Abstract
AbstractWe generalise results of Buzzard, Taylor and Kassaei on analytic continuation ofp-adic overconvergent eigenforms over ℚ to the case ofp-adic overconvergent Hilbert eigenforms over totally real fields F, under the assumption thatpsplits completely in F. This includes weight-one forms and has applications to generalisations of Buzzard and Taylor’s main theorem. Next, we follow an idea of Kassaei’s to generalise Coleman’s well-known result that ‘an overconvergentUp-eigenform of small slope is classical’ to the case ofp-adic overconvergent Hilbert eigenforms of Iwahori level.
Subject
Algebra and Number Theory
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