Products of vector valued Eisenstein series
Products of vector valued Eisenstein series
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矢量值Eisenstein系列的乘积
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：
Martin Westerholt
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文献类型：
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作者：
Martin Westerholt
本文证明了至多两个起源于水平1的向量值Eisenstein级数的乘积，对于同余子群，可以跨越所有尖点型空间。这可以被看作是一个类似的水平方面的结果，可以追溯到兰金，和Kohnen和Zagier，侧重于重量方面。证明的主要特征是向量值Hecke算子。我们从它们中恢复了几个经典的构造，包括经典的Hecke算子，Atkin-Lehner对合和旧形式。作为我们的主要定理的推论，我们得到了一个消失的条件，让人想起由Kohnen和Zagier在他们先前提到的结果的上下文中推导出的周期关系的模形式。
Abstract We prove that products of at most two vector valued Eisenstein series that originate in level 1 span all spaces of cusp forms for congruence subgroups. This can be viewed as an analogue in the level aspect to a result that goes back to Rankin, and Kohnen and Zagier, which focuses on the weight aspect. The main feature of the proof are vector valued Hecke operators. We recover several classical constructions from them, including classical Hecke operators, Atkin–Lehner involutions, and oldforms. As a corollary to our main theorem, we obtain a vanishing condition for modular forms reminiscent of period relations deduced by Kohnen and Zagier in the context their previously mentioned result.