论文标题
仅使用Riemann Zeta函数的零零来迈向普遍的Riemann假设
Towards the Generalized Riemann Hypothesis using only zeros of the Riemann zeta function
论文作者
论文摘要
对于[\ tfrac12,1）$中的任何真正的$β_0\，令$ {\ rm grh} [β_0] $是每个dirichlet themert $χ$和所有零$ρ=β+iγ$ l（s，c）$β\ leleβ_0$（尤其是）的断言grh} [\ frac12] $是普遍的Riemann假设）。在本文中，我们表明$ {\ rm grh} [\ frac {9} {10}] $的有效性仅取决于Riemann Zeta Zeta函数$ζ（S）$的零的某些分布属性。非主体dirichlet $ l $ functions的零没有任何条件。
For any real $β_0\in[\tfrac12,1)$, let ${\rm GRH}[β_0]$ be the assertion that for every Dirichlet character $χ$ and all zeros $ρ=β+iγ$ of $L(s,χ)$, one has $β\leβ_0$ (in particular, ${\rm GRH}[\frac12]$ is the Generalized Riemann Hypothesis). In this paper, we show that the validity of ${\rm GRH}[\frac{9}{10}]$ depends only on certain distributional properties of the zeros of the Riemann zeta function $ζ(s)$. No conditions are imposed on the zeros of nonprincipal Dirichlet $L$-functions.
