论文标题
如果$ l（χ，1）= 0 $，则$ζ（1/2+it）\ neq0 $
If $L(χ,1)=0$ then $ζ(1/2+it)\neq0$
论文作者
论文摘要
令$ l（s）= \ sum_ {n = 1}^{+\ infty} \ dfrac {a（n）} {n^s} $ be dirichlet系列是$ a（n）$是一个有界的完全乘法函数。我们证明，如果$ l（s）$扩展到开放的半空间$ \ re s> 1-δ$，$Δ> 0 $和$ l（1）= 0 $的全体形态功能，那么这样的半空间是Riemann Zeta Zeta函数$ Zera的零免费区域。对于在有限程度的数字字段的代数整数的理想空间中定义的完全乘法函数证明了类似的结果。
Let $L(s)=\sum_{n=1}^{+\infty}\dfrac{a(n)}{n^s}$ be a Dirichlet series were $a(n)$ is a bounded completely multiplicative function. We prove that if $L(s)$ extends to a holomorphic function on the open half space $\Re s >1-δ$, $δ>0$ and $L(1)=0$ then such a half space is a zero free region of the Riemann zeta function $ζ(s)$. Similar results is proven for completely multiplicative functions defined on the space of the ideals of the ring of the algebraic integers of a number field of finite degree.
