An isomorphism between scalar-valued modular forms and modular forms for Weil representations
An isomorphism between scalar-valued modular forms and modular forms for Weil representations
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标量值模形式与 Weil 表示的模形式之间的同构
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发表时间：
2013
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通讯作者：
Yichao Zhang
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作者：
Yichao Zhang
本文考虑由实二次域的范数形式给出的判别形式及其引申的Weil表示。证明了在自同构群作用下不变的Weil表示的向量值模形式空间与满足$$epsilon $$ ϵ-condition条件的标量值模形式空间之间存在同构，并由此将Borcherds的障碍物定理转化为标量值模形式。最后，我们考虑一个级别$$12$$ 12的例子。
In this paper, we consider discriminant forms that are given by the norm form of real quadratic fields and their induced Weil representations. We prove that there exists an isomorphism between the space of vector-valued modular forms for the Weil representations that are invariant under the action of the automorphism group and the space of scalar-valued modular forms that satisfy some $$epsilon $$ϵ-condition, with which we translate Borcherds’s theorem of obstructions to scalar-valued modular forms. In the end, we consider an example in the case of level $$12$$12.