论文标题
Riemann假设的局部几何证明
Local geometric proof of Riemann Hypothesis
论文作者
论文摘要
riemann函数$ξ（s）= u+iv，s =β+1/2+it $具有重要的对称性：$ v = 0 $如果$β= 0 $。对于$β> 0 $，我们证明$ | u |> 0 $内部的任何root-Interval $ i_j = [t_j，t_j，t_ {j+1}] $，$ v $在两个端点的$ i_j $的端点相反。它们意味着本地峰值谷结构和$ ||ξ|| = | u |+|+| v/β|> 0 $ in $ i_j $。因为每个$ t $都必须在某些$ i_j $中，然后$ ||ξ||> 0 $对于任何$ t $都是有效的。根据u re re（\ frac {ξ'}ξ）> 0 $的等价$，我们表明Rhe Rhe含义了峰值 - valley结构，这可能是Bombieri（2000）期望的几何模型。
Riemann function $ξ(s)=u+iv, s=β+1/2+it$ has the important symmetry: $v=0$ if $β=0$. For $β>0$ we prove $|u|>0$ inside any root-interval $I_j=[t_j,t_{j+1}]$ and $v$ has opposite signs at two end-points of $I_j$. They imply local peak-valley structure and $||ξ||=|u|+|v/β|>0$ in $I_j$. Because each $t$ must lie in some $I_j$, then $||ξ||>0$ is valid for any $t$. By the equivalence $Re(\frac{ξ'}ξ)>0$ of Lagarias(1999), we show that RH implies the peak-valley structure,which may be the geometric model expected by Bombieri(2000).
