Rendiconti del Seminario Matematico della Università di Padova


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Volume 132, 2014, pp. 133–229
DOI: 10.4171/RSMUP/132-10

Published online: 2014-11-04

Classicality of overconvergent Hilbert eigenforms: case of quadratic residue degrees

Yichao Tian[1]

(1) Chinese Academy of Sciences, Beijing, China

Let $ F$ be a real quadratic field, $ p$ be a rational prime inert in $ F$, and $ N\geq 4$ be an integer coprime to $ p$. Consider an overconvergent $ p$-adic Hilbert eigenform $ f$ for $ F$ of weight $ (k_ 1,k_ 2)\in {\bf Z} ^{2}$ and level $ {\it \Gamma} _ {00}(N)$. We prove that if the slope of $ f$ is strictly less than $ \min \{k_ 1,k_ 2\}-2$ , then $ f$ is a classical Hilbert modular form of level $ {\it \Gamma} _ {00}(N)\cap {\it \Gamma} _ {0}(p)$ .

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Tian Yichao: Classicality of overconvergent Hilbert eigenforms: case of quadratic residue degrees. Rend. Sem. Mat. Univ. Padova 132 (2014), 133-229. doi: 10.4171/RSMUP/132-10