论文标题
试图证明Riemann假设的证明
An attempt of proof of Riemann Hypothesis
论文作者
论文摘要
本文介绍了Riemann假设（RH）的证明。令$ t> 10^{10} $任意大。让区域$ | big \ {z = x+i y \ \ big | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0} <x <1，\ 0 <y <y <t \ big \ \} $。本文的目的是证明$ n_t = 0 $。假设$ n_t> 0 $。至少存在一个根$ρ= \ frac {1} {2}+{\ bf u}+iγ$，其实际部分更大或等于$ω_t$中所有其他根的实际部分。令$ v \ geq \ frac {3} {2} $。令$ \ varepsilon> 0 $任意小。我们证明$ f（z）= \ frac {ζ'（z）} {ζ（z）} $在开放式磁盘$ω__\ varepsilon = \ big | big | z- \ big | z- \ big big（ρ+frac {\ varepsilon} $ s =ρ+\ varepsilon $。我们从$ζ（s）$的泰勒系列中证明了$ f（s）\ sim \ sim \ frac {1} {\ varepsilon} \ rightarrow \ rightarrow \ infty $当$ \ varepsilon \ rightArrow 0 $ 0 $，以及通过$ f（s）$ f（s）$ f（s）$ f（s） $ f（s）= f（c_0） - （v- \ frac {\ varepsilon} {2}）f'（c_0） +\ frac {（v- \ \ frac {\ varepsilon} {2}）^2} {2！} f''（c_0） - \ frac {（v- \ frac {\ frac {\ varepsilon}对于\} c_0 =ρ+\ frac {\ varepsilon} {2}+v，$ in $ω__\ varepsilon $，$ f（s）\ not \ not \ rightArrow \ rightArrow \ rightArrow \ infty $当$ \ varepsilon \ varepsilon \ varepsilon \ rightarrow 0 $，构成我们允许我们允许我们使用Prove RH的矛盾。
This paper deals with an attempt of proof of the Riemann Hypothesis (RH). Let $T>10^{10}$ arbitrarily large. Let the region $Ω_T=\Big\{z=x+i y\ \Big|\ \frac{1}{2}<x<1, \ 0<y<T\Big\}.$ There is a finite number $N_T$ of roots of $ζ(z)$ in $Ω_T$. The aim of the paper is to prove that $N_T=0$. Suppose that $N_T>0$. There exists at least one root $ρ=\frac{1}{2}+{\bf u}+iγ$ whose real part is greater or equal to the real part of all the other roots in $Ω_T$. Let $v\geq \frac{3}{2}$. Let $\varepsilon>0$ arbitrarily small. We prove that $f(z)=\frac{ζ'(z)}{ζ(z)}$ is analytic in the open disk $Ω_\varepsilon=\Big\{ \Big|z-\Big(ρ+\frac{\varepsilon}{2}+v\Big)\Big|\Big\}< v.$ Let $s=ρ+\varepsilon$. We prove, from the Taylor series of $ζ(s)$, that $f(s)\sim \frac{1}{\varepsilon}\rightarrow \infty$ when $\varepsilon\rightarrow 0$, and that, through the representation of $f(s)$ as a Taylor series, $f(s)=f(c_0)-(v-\frac{\varepsilon}{2})f'(c_0) +\frac{(v-\frac{\varepsilon}{2})^2}{2!}f''(c_0)-\frac{(v-\frac{\varepsilon}{2})^3}{3!}f^{(3)}(c_0)+\dots\mbox{\ for\ }c_0=ρ+\frac{\varepsilon}{2}+v,$ in $Ω_\varepsilon$, that $f(s)\not\rightarrow \infty$ when $\varepsilon\rightarrow 0$, a contradiction which allows us to prove RH.
