论文标题
o（1,5）上盖的明确提升构造
An explicit lifting construction of CAP forms on O(1,5)
论文作者
论文摘要
我们在签名（1+，5-）的正交组的O（1,5）上明确构建非脾气尖缘。 Given a definite quaternion algebra B over $\mathbb{Q}$, the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of B. Our construction can be viewed as a generalization of [22] to the case of any definite quaternion algebras, for which we note that [22] takes up the case where the discriminant of B是两个。与[22]不同，结构的方法是考虑到Borcherds制定后，考虑从Maass Cusp形式到O（1,5）的theta提升。详细研究了由我们的风口尖锐形式产生的尖尖代表。我们确定了尖锐表示的所有局部组成部分，并表明我们的尖cusp形式是CAP形式。
We explicitly construct non-tempered cusp forms on the orthogonal group O(1,5) of signature (1+,5-). Given a definite quaternion algebra B over $\mathbb{Q}$, the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of B. Our construction can be viewed as a generalization of [22] to the case of any definite quaternion algebras, for which we note that [22] takes up the case where the discriminant of B is two. Unlike [22] the method of the construction is to consider the theta lifting from Maass cusp forms to O(1,5), following the formulation by Borcherds. The cuspidal representations generated by our cusp forms are studied in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms.
