论文标题
高度统一的质数定理
Highly Uniform Prime Number Theorems
论文作者
论文摘要
我们证明了特定类别的$ l $ functions的质数定理的高度均匀版本。 $ x $的范围在多项式取决于分析导体，而误差项根据优化问题表示，取决于可用的无零区域。该类包含兰金 - 塞尔伯格$ l $ -function $ l（s，π\ timesπ'）$与cuspidal automorphic表示相关的$π$和$π'我们的主要结果意味着完全通用性（具有分析导体均匀性）的第一个统一质数定理。
We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explicitly on the available zero-free region. The class contains the Rankin-Selberg $L$-function $L(s,π\times π')$ associated to cuspidal automorphic representations $π$ and $π'$ of $\mathrm{GL}_{m}$ and $\mathrm{GL}_{m'}$, respectively. Our main result implies the first uniform prime number theorems for such $L$-functions (with analytic conductor uniformity) in complete generality.
