Non-vanishing of Miyawaki type lifts
Non-vanishing of Miyawaki type lifts
复制标题
宫胁式电梯的不消失
DOI：
10.1007/s12188-019-00207-6
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Takuya
中科院分区：
文献类型：
--
作者：
Kim;Henry H.; Yamauchi;Takuya
在本文中，我们研究了宫胁式升力在各种情况下的不消失现象。在 Kim 和 Yamauchi 构建的 GSpin(2, 10) 的情况下（Math Z 288(1–2):415–437, 2018），我们利用了恒等处的傅里叶系数与两个椭圆尖点形式的 Rankin-SelbergL 函数密切相关的事实。在 Siegel 尖点形式的原始 Miyawaki 升力的情况下，我们使用某些傅里叶系数是 Petersson 内积这一事实，这是不平凡的。这提供了无数非零 Miyawaki 升力的例子。我们给出了 24 次和权重 24 的明确示例。我们还证明了酉群的 Miyawaki 提升的类似结果。特别是，我们针对eachmod 4获得了宫胁升力不消失的无条件结果。在上一节中，我们证明了无限多个半积分权重西格尔尖点形式的宫胁升力不消失。我们给出了 16 阶和权重的明确示例。
In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case ofGSpin(2, 10) constructed in Kim and Yamauchi (Math Z 288(1–2):415–437, 2018), we use the fact that the Fourier coefficient at the identity is closely related to the Rankin–SelbergL-function of two elliptic cusp forms. In the case of the original Miyawaki lifts of Siegel cusp forms, we use the fact that certain Fourier coefficients are the Petersson inner product which is non-trivial. This provides infinitely many examples of non-zero Miyawaki lifts. We give explicit examples of degree 24 and weight 24. We also prove a similar result for Miyawaki lifts for unitary groups. Especially, we obtain an unconditional result on non-vanishing of Miyawaki lifts forfor eachmod 4. In the last section, we prove the non-vanishing of the Miyawaki lifts for infinitely many half-integral weight Siegel cusp forms. We give explicit examples of degree 16 and weight.