论文标题
朝着$ \ mathrm {gl} _ {n} $的深度riemann假设
Towards the Deep Riemann Hypothesis for $\mathrm{GL}_{n}$
论文作者
论文摘要
我们在关键行上的标准$ l $ functions的标准欧拉产品的收敛性上阐述了通用线性$ \ mathrm {gl} _ {n} $的深层riemann假设。它有条件地改善了质数定理中的误差项，超出了Riemann假设的预测。此外，我们从深层假设的角度讨论了$ \ mathrm {gl} _ {n} $上的satake参数的chebyshev偏见。
We explicate the deep Riemann hypothesis for the general linear group $\mathrm{GL}_{n}$ on the convergence of normalised Euler products of standard $L$-functions on the critical line. It conditionally improves upon the error term in the prime number theorem beyond what the grand Riemann hypothesis predicts. Furthermore, we discuss the Chebyshev bias for Satake parameters on $\mathrm{GL}_{n}$ from the perspective of the deep Riemann hypothesis.
