In this paper we study the analytic properties of the standard L-function attached to vector valued quaternionic modular forms using the Rankin-Selberg method. This involves the construction of vector valued theta series, which we obtain by applying some differential operators on Jacobi-theta series studied by Krieg. Such differential operators are obtained from the Howe-Weyl duality for the pair $S{p}_n(\mathbb{C})\times G{L}_{2n}(\mathbb{C})$.

中文翻译：

---

在标准L功能上附加到四元离子模块化形式。

在本文中，我们使用Rankin-Selberg方法研究了附加到矢量值四元离子模块形式上的标准L函数的解析性质。这涉及向量值theta级数的构造，我们通过在Krieg研究的Jacobi-theta级数上应用一些微分算子来获得。这样的微分算子是从对的Howe-Weyl对偶获得的$\mathrm{小号}{p}_{ñ}（\mathbb{C}）\times G{\mathrm{大号}}_{2ñ}（\mathbb{C}）$。