In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case of GSpin(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–Selberg L-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 for $$U(n+1,n+1)$$ for each $$n\equiv 3$$ mod 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 $$\frac{29}{2}$$.

中文翻译：

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宫胁型电梯的不消失

在本文中，我们研究了宫胁型电梯在各种情况下的不消失。在 Kim 和 Yamauchi (Math Z 288(1-2):415-437, 2018) 中构建的 GSpin(2, 10) 的情况下，我们使用的事实是，身份处的傅立叶系数与 Rankin-两个椭圆尖峰形式的 Selberg L 函数。在 Siegel 尖点形式的原始 Miyawaki 提升的情况下，我们使用某些傅立叶系数是非平凡的 Petersson 内积这一事实。这提供了无数非零宫胁电梯的例子。我们给出了度数 24 和权重 24 的明确例子。我们还证明了宫胁升降机对于酉群的类似结果。特别是，对于每个 $$n\equiv 3$$ mod 4，我们在 $$U(n+1,n+1)$$ 的情况下获得了宫胁电梯不消失的无条件结果。在最后一节中，我们证明了对于无限多个半积分重量 Siegel 尖点形式的 Miyawaki 升降机的不消失。我们给出了 16 次和权重 $$\frac{29}{2}$$ 的明确示例。