标题： 共周期和中心对称立方体L值 显示英文标题

标题： Co-periods and central symmetric cube L-values

摘要： 在本文中，我们研究与$\GL(2)$上的自守形式相关的共周期积分以及三次 Kazhdan-Patterson 覆盖$\GL(2)$上的两个特殊θ级数。在局部方面，我们证明$\Hom$空间总是维一的，并进行了无ramified 计算。在整体方面，我们给出了Eisenstein级数的共周期积分的欧拉分解，并提出了一个类似Ichino-Ikeda的猜想，将尖点形式的共周期积分与对称立方$L$函数的中心临界值相关联。我们还从局部重数一的结果推导出存在具有指定局部成分且中心对称立方$L$值不为零的尖点自守形式。 显示英文摘要

摘要： In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the central critical value of symmetric cube $L$-functions. We also deduce from the local multiplicity one result that there exist cuspidal automorphic forms with prescribed local components and non-vanishing central symmetric cube $L$-values.