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Analytic continuation of overconvergent Hilbert eigenforms in the totally split case

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  02 February 2010

Shu Sasaki
Shu Sasaki*
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 5311 Bonn, Germany (email: s.sasaki.03@cantabgold.net)
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Abstract

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

Keywords

p-adic modular formsHilbert modular varieties

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11G18: Arithmetic aspects of modular and Shimura varieties 14G22: Rigid analytic geometry 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 3 , May 2010 , pp. 541 - 560
Copyright
Copyright © Foundation Compositio Mathematica 2010

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