Author(s)

Xiang Liu¹, Rybachuk Ekaterina², Fasheng Liu^3*

¹Tong Ji University, Shanghai, China.
²Kuzbass State Technical University, Kemerovo, Russia.
³Shandong University of Science and Technology, Qingdao, China.

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.

Theta-Series, Jacobi Functional Equation, Schwarz Reflection Principle, Riemann Hypothesis (RH)

Liu, X. , Ekaterina, R. and Liu, F. (2016) A Direct Proof for Riemann Hypothesis Based on Jacobi Functional Equation and Schwarz Reflection Principle. Advances in Pure Mathematics, 6, 193-200. doi: 10.4236/apm.2016.64016.