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The exceptional zero conjecture for Hilbert modular forms

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 January 2009

Chung Pang Mok
Chung Pang Mok*
Affiliation:
970 Evans, University of California, Berkeley, CA 94720-3840, USA (email: [email protected])
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Abstract

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Using a p-adic analogue of the convolution method of Rankin–Selberg and Shimura, we construct the two-variable p-adic L-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg–Stevens [R. Greenberg and G. Stevens, p-adic L-functions and p-adic periods of modular forms, Invent. Math. 111 (1993), 407–447] are satisfied, from which we deduce special cases of the Mazur–Tate–Teitelbaum conjecture in the Hilbert modular setting.

Keywords

Hilbert modular formsp-adic L-functionsexceptional zero conjecture

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 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 1 - 55
Copyright
Copyright © Foundation Compositio Mathematica 2009

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