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Fourier coefficients of the overconvergent generalized eigenform associated to a CM form
International Journal of Number Theory ( IF 0.7 ) Pub Date : 2019-12-18 , DOI: 10.1142/s1793042120500608
Chi-Yun Hsu 1
Affiliation  

Let [Formula: see text] be a modular form with complex multiplication. If [Formula: see text] has critical slope, then Coleman’s classicality theorem implies that there is a [Formula: see text]-adic overconvergent generalized Hecke eigenform with the same Hecke eigenvalues as [Formula: see text]. We give a formula for the Fourier coefficients of this generalized Hecke eigenform. We also investigate the dimension of the generalized Hecke eigenspace of [Formula: see text]-adic overconvergent forms containing [Formula: see text].

中文翻译:

与 CM 形式相关的过收敛广义特征形式的傅立叶系数

令 [公式:见正文] 为复数乘法的模形式。如果 [Formula: see text] 具有临界斜率,则 Coleman 经典性定理意味着存在 [Formula: see text]-adic 过收敛广义 Hecke 特征型,其 Hecke 特征值与 [Formula: see text] 相同。我们给出了这个广义 Hecke 特征型的傅立叶系数的公式。我们还研究了 [Formula: see text]-adic overconvergent forms 的广义 Hecke 特征空间的维数,其中包含 [Formula: see text]。
更新日期:2019-12-18
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