论文标题
朝向$ \ mathrm {gl} _n $变体
Towards a $\mathrm{GL}_n$ variant of the Hoheisel phenomenon
论文作者
论文摘要
令$π$为$ \ mathrm {gl} _n $在一个数字字段上的统一cuspidal自动形态表示，让$ \tildeπ$与$π$相关。我们证明了正确订单的有效上限和下限，在兰金 - 塞尔伯格$ l $ -function $ l（s，π\ times \tildeπ）$的简短间隔素数定理中，扩展了Hoheisel和Linnik的工作。一路上，我们首次证明$ l（s，π\ times \widetildeπ）$除了可能的landau-siegel零外，没有任何无条件的无条件零区域。
Let $π$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_n$ over a number field, and let $\tildeπ$ be contragredient to $π$. We prove effective upper and lower bounds of the correct order in the short interval prime number theorem for the Rankin-Selberg $L$-function $L(s,π\times\tildeπ)$, extending the work of Hoheisel and Linnik. Along the way, we prove for the first time that $L(s,π\times\widetildeπ)$ has an unconditional standard zero-free region apart from a possible Landau-Siegel zero.
