论文标题
Rankin-Selberg卷积的第二瞬间，转移了Dirichlet系列
Second moments of Rankin-Selberg convolution and shifted Dirichlet series
论文作者
论文摘要
在本文中，我们对任何$ n $的$γ_0（n）$工作，并在关键行$ \ frac {1} {1} {1} {1} {2}+它作为主要术语以及在$ t $方面和光谱方面的急剧误差期限的一般点上写下两个不同的兰金·塞尔伯格卷积的频谱时刻。结果，我们在$ t $和光谱方面获得了混合Weyl型亚凸度。此外，对于固定模块化表单$ f $，$ g $均匀重量$ k \ geq 4 $，我们显示存在maass cusp form $ u_j $，以便$ l（1/2，f \ times u_j）$，$ l（1/2，g \ g \ times u_j）$同时是非零的。
In this paper we work over $Γ_0(N)$, for any $N$ and write the spectral moment of a product of two distinct Rankin-Selberg convolutions at a general point on the critical line $\frac{1}{2}+it$ as a main term plus a sharp error term in the $t$ aspect and the spectral aspect. As a result we obtain hybrid Weyl type subconvexity results in the $t$ and spectral aspects. Also, for fixed modular forms $f$, $g$ of even weight $k\geq 4$ we show there exists a Maass cusp form $u_j$ such that $L(1/2, f\times u_j)$, $L(1/2, g\times u_j)$ are simultaneous non-zero.
