论文标题
Riemann Zeta函数的所有复杂零都在关键线上：Riemann假设的两个证明
All Complex Zeros of the Riemann Zeta Function Are on the Critical Line: Two Proofs of the Riemann Hypothesis
论文作者
论文摘要
我提供了两个独立的证据，证明了许多数学中最大的未解决问题所认为的Riemann假设。我发现Riemann Zeta函数的复杂零的可接受域是关键线。本文的方法和结果基于关于复杂值函数的零数的众所周知的定理（Jensen，Titchmarsh，Rouche定理），其中Riemann映射定理充当复杂平面上的单位磁盘之间的桥梁。通过主要依靠复杂分析的众所周知的定理，我们的方法使本文可以访问相对较大的受众允许快速检查其有效性。这两个证明都不使用Riemann Zeta函数的任何功能方程，除了利用其隐含的对称性对临界条上的非平凡零的对称性。
I present two independent proofs of the Riemann Hypothesis considered by many the greatest unsolved problem in mathematics. I find that the admissible domain of complex zeros of the Riemann Zeta Function is the critical line. The methods and results of this paper are based on well-known theorems on the number of zeros for complex value functions (Jensen, Titchmarsh, Rouche theorems), with the Riemann Mapping Theorem acting as a bridge between the Unit Disk on the complex plane and the critical strip. By primarily relying on well-known theorems of complex analysis our approach makes this paper accessible to a relatively wide audience permitting a fast check of its validity. Both proofs do not use any functional equation of the Riemann Zeta Function, except leveraging its implied symmetry for non-trivial zeros on the critical strip.
