In this article we obtain an explicit formula for certain Rankin-Selberg type Dirichlet series associated to certain Siegel cusp forms of half-integral weight. Here these Siegel cusp forms of half-integral weight are obtained from the composition of the Ikeda lift and the Eichler-Zagier-Ibukiyama correspondence. The integral weight version of the main theorem had been obtained by Katsurada and Kawamura. The result of the integral weight case is a product of $L$-function and Riemann zeta functions, while half-integral weight case is a infinite summation over negative fundamental discriminants with certain infinite products. To calculate explicit formula of such Rankin-Selberg type Dirichlet series, we use a generalized Maass relation and adjoint maps of index-shift maps of Jacobi forms.

中文翻译：

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RANKIN-SELBERG 型的特定 DiRICHLET 系列与 IKEDA 半积分升降机相关联

在本文中，我们获得了与某些半积分权的某些 Siegel 尖点形式相关的某些 Rankin-Selberg 型狄利克雷级数的明确公式。在这里，这些半积分重量的 Siegel 尖峰形式是从 Ikeda 电梯和 Eichler-Zagier-Ibukiyama 对应关系的组成中获得的。Katsurada 和 Kawamura 已经获得了主定理的积分权版本。积分权情况的结果是$L$-函数和黎曼zeta函数的乘积，而半积分权情况是负基本判别式与某些无限乘积的无限求和。为了计算这种 Rankin-Selberg 型 Dirichlet 级数的显式公式，我们使用广义 Maass 关系和 Jacobi 形式的索引偏移映射的伴随映射。