Compositio Mathematica

Research Article

Analytic continuation of overconvergent Hilbert eigenforms in the totally split case

Shu Sasakia1

a1 Max-Planck-Institut für Mathematik, Vivatsgasse 7, 5311 Bonn, Germany (email: s.sasaki.03@cantabgold.net)

Abstract

We generalise results of Buzzard, Taylor and Kassaei on analytic continuation of p-adic overconvergent eigenforms over xs211A 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

  • 11F33;
  • 11F41 (primary);
  • 11G18;
  • 14G22;
  • 14G35 (secondary)

Keywords

  • p-adic modular forms;
  • Hilbert modular varieties

Footnotes

This work was supported by a EPSRC project grant.