a1 Max-Planck-Institut für Mathematik, Vivatsgasse 7, 5311 Bonn, Germany (email: email@example.com)
We generalise results of Buzzard, Taylor and Kassaei on analytic continuation of p-adic overconvergent eigenforms over to the case of p-adic overconvergent Hilbert eigenforms over totally real fields F, under the assumption that p splits 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 overconvergent Up-eigenform of small slope is classical’ to the case of p-adic overconvergent Hilbert eigenforms of Iwahori level.
(Received May 05 2008)
(Accepted August 16 2009)
(Online publication February 02 2010)
2000 Mathematics Subject Classification
This work was supported by a EPSRC project grant.