SSRN Author: Roberto VioliRoberto Violi SSRN Content
https://privwww.ssrn.com/author=331701
https://privwww.ssrn.com/rss/en-usThu, 04 Feb 2021 01:13:09 GMTeditor@ssrn.com (Editor)Thu, 04 Feb 2021 01:13:09 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: All Complex Zeros of the Riemann Zeta Function Are on the Critical Line: Two Proofs of the Riemann HypothesisIn this paper, 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 given by ℜ(s)=1/2. Results of this paper are based on well-known theorems on the number of zeros for complex value functions (Jensen’s, Titchmarsh’s, Rouché’s theorem), 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 zeroes on the critical strip.
https://privwww.ssrn.com/abstract=3716517
https://privwww.ssrn.com/1987309.htmlWed, 03 Feb 2021 09:47:14 GMTREVISION: All Complex Zeroes of the Riemann Zeta Function Are on the Critical Line: Two Proofs of the Riemann HypothesisIn this paper, 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 zeroes of the Riemann Zeta-Function is the critical line given by ℜ(s)=1/2. Methods and results of this paper are based on well-known theorems on the number of zeroes for complex value functions (Jensen’s, Titchmarsch’s and Rouché’s theorem), 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 zeroes on the critical strip.
https://privwww.ssrn.com/abstract=3716517
https://privwww.ssrn.com/1974225.htmlTue, 22 Dec 2020 15:42:11 GMT