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A Direct Proof for Riemann Hypothesis Based on Jacobi Functional Equation and Schwarz Reflection Principle
Tong Ji University, Shanghai, China
Kuzbass State Technical University, Kemerovo, Russia
Shandong University of Science and Technology, Qingdao, China
- 1 Tong Ji University, Shanghai, China
- 2 Kuzbass State Technical University, Kemerovo, Russia
- 3 Shandong University of Science and Technology, Qingdao, China
Advances in Pure Mathematics·Volume 06 (2016)·Pages 193–200·Published 15 March 2016·DOI10.4236/apm.2016.64016
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Abstract
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.
KeywordsTheta-SeriesJacobi Functional EquationSchwarz Reflection PrincipleRiemann Hypothesis (RH)
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