P ‐adic L ‐functions of Bianchi modular forms
P ‐adic L ‐functions of Bianchi modular forms
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Bianchi 模形式的 P 进 L 函数
DOI：
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发表时间：
2014
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影响因子：
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通讯作者：
Chris Williams
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文献类型：
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作者：
Chris Williams
由Rob Pollack和Glenn Stevens发展的过收敛模符号理论给出了模形式的p进L-函数的一个美丽而有效的构造。本文对比安奇模形式，即虚二次域上的模形式，给出了他们结果的一个类似。特别是，我们证明了控制定理，说，典型的专业化地图从过收敛到经典的比安奇模块化符号是一个同构的小斜率特征空间的合适的Hecke运营商。给出了比安奇模形式的经典模符号与其L-函数的临界值之间的一个明确联系，从而可以构造比安奇模形式的p进L-函数.
The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p ‐adic L ‐function of a modular form. In this paper, we give an analogue of their results for Bianchi modular forms, that is, modular forms over imaginary quadratic fields. In particular, we prove control theorems that say that the canonical specialisation map from overconvergent to classical Bianchi modular symbols is an isomorphism on small slope eigenspaces of suitable Hecke operators. We also give an explicit link between the classical modular symbol attached to a Bianchi modular form and critical values of its L ‐function, which then allows us to construct p ‐adic L ‐functions of Bianchi modular forms.