论文标题
兰金·塞尔伯格（Rankin-Selberg）$ l $ functions在关键带的边缘的下限
Lower Bounds for Rankin-Selberg $L$-functions on the Edge of the Critical Strip
论文作者
论文摘要
令$ f $为一个数字字段，让$π_1$和$π_2$是$ \ operatoTorname {gl} _ {n_1}（\ MathBb {a} _f）$ and $ \ perperatoReOnnAme and $ peratatorNORNAME {gl} _ $ {n_2 _2 _2}（n _2 _2} _ {n_2 _2}（\ a $} { 分别。在本文中，我们沿着$ t $ - appect中关键条的边缘$ \ re s沿边缘$ \ re s沿边缘$ \ re s沿边缘$ \ re s沿着$ t $ - 广告中的critist $ s = 1 $的新的下限$ l（s，π_1\ times \ times \widetildeπ_2）$。还确定了$ l（s，π_1\ times \widetildeπ_2）$的相应零区域。
Let $F$ be a number field, and let $π_1$ and $π_2$ be distinct unitary cuspidal automorphic representations of $\operatorname{GL}_{n_1}(\mathbb{A}_F)$ and $\operatorname{GL}_{n_2}(\mathbb{A}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s, π_1 \times \widetildeπ_2)$ along the edge $\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, π_1 \times \widetildeπ_2)$ is also determined.
