论文标题
通过分析函数空间的ζ功能的零半平面
Zero-free half-planes of the ζ-function via spaces of analytic functions
论文作者
论文摘要
在本文中，我们介绍了一种通用方法，用于通过识别具有特定属性的分析函数的拓扑矢量空间来推导Riemann Zeta函数$ζ$的零半平面。此方法应用于加权$ \ ell^2 $空间和经典的Hardy Spaces $ H^P $（$ 0 <P \ leq2 $）。因此，对于$ζ$函数的零半平面的存在获得了确切的条件。
In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $ζ$ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to weighted $\ell^2$ spaces and classical Hardy spaces $ H^p $ ($ 0<p\leq2 $). As a consequence precise conditions are obtained for the existence of zero-free half planes for the $ζ$-function.
