A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lift of half-integral weight
A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lift of half-integral weight
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与半积分重量池田升力相关的Rankin-Selberg型狄利克雷级数
DOI：
10.1112/s0025579319000172
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发表时间：
2019
期刊：
影响因子：
0.8
通讯作者：
Shuichi Hayashida
中科院分区：
文献类型：
--
作者：
Hisanori Ohashi;Masayuki Kawakita;Shuichi Hayashida
本文得到了与一类半整数权的Siegel尖点形式相关的Rankin-Selberg型Dirichlet级数的一个显式公式。这里，这些半整数权的Siegel尖点形式是由Ikeda升力和Eichler-Zagier-Ibukiyama对应的组合得到的。主要定理的整权形式是由Katsurada和Kawamura得到的。整权情形的结果是an-函数和Riemann Zeta函数的乘积，而半整权情形是负基本判别式与某些无穷积的无穷和。为了计算这类Rankin-Selberg型Dirichlet级数的显式公式，我们利用广义Maass关系和Jacobi型指数移位映射的伴随映射。
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 was obtained by Katsurada and Kawamura. The result of the integral weight case is a product of an ‐function and Riemann zeta functions, while the half‐integral weight case is an infinite summation over negative fundamental discriminants with certain infinite products. To calculate an explicit formula for such Rankin–Selberg type Dirichlet series, we use a generalized Maass relation and adjoint maps of index‐shift maps of Jacobi forms.