In this work, we use the Rankin–Selberg method to obtain results on the analytic properties of the standard L-function attached to vector-valued Siegel modular forms. In particular we provide a detailed description of its possible poles and obtain a non-vanishing result of the twisted L-function beyond the usual range of absolute convergence. Our results include also the case of metaplectic Siegel modular forms. We remark that these results were known in this generality only in the case of scalar weight Siegel modular forms. As an interesting by-product of our work we establish the cuspidality of some theta series.

中文翻译：

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关于向量值 Siegel 模形式的 Rankin-Selberg 方法

在这项工作中，我们使用 Rankin-Selberg 方法来获得标准分析性质的结果大号- 附加到向量值 Siegel 模形式的函数。特别是我们提供了它可能的极点的详细描述，并获得了扭曲的非消失结果大号-函数超出通常的绝对收敛范围。我们的结果还包括 metaplectic Siegel 模形式的情况。我们注意到，这些结果仅在标量权 Siegel 模形式的情况下才普遍知道。作为我们工作的一个有趣的副产品，我们建立了一些 theta 系列的 cuspidality。