负权向量值模拟模形式的局部Maas形式和Eichler-Selberg关系

Pub Date : 2021-08-30 DOI:10.2140/pjm.2023.322.381

Joshua Males, Andreas Mono

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引用次数: 2

摘要

通过比较签名$(r,s)$的偶格上修正的(\ {a} la Borcherds)较高Siegel theta提升的两种不同的求值，我们证明了一类广泛的负权向量值模拟模形式的Eichler—Selberg型关系。在此过程中，我们详细介绍了升力的几个性质，并证明了它在某些签名的格拉斯曼子上产生无限族的局部(和局部调和)Maa{\ss}形式。

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Local Maass forms and Eichler–Selberg relations for negative-weight vector-valued mock modular forms

By comparing two different evaluations of a modified (\`{a} la Borcherds) higher Siegel theta lift on even lattices of signature $(r,s)$, we prove Eichler--Selberg type relations for a wide class of negative weight vector-valued mock modular forms. In doing so, we detail several properties of the lift, as well as showing that it produces an infinite family of local (and locally harmonic) Maa{\ss} forms on Grassmanians in certain signatures.

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