A Simple Rigorous Proof of Riemann’s Hypothesis via Reflection Symmetry

We present a simple rigorous proof of Riemann’s hypothesis. This hypothesis has remained unsolved since Riemann’s original formulation in 1859, although numerous zeros have been found along the critical line with the assistance of computer calculations. Our analytic proof is based on the analysis of the reflection symmetry between |Γ(s⁄2))〖(ζ(s))⁄π^(s⁄2) |〗^2 and |Γ(((1-s))⁄2)) 〖ζ(1-s)⁄π^(((1-s))⁄2) |〗^2, although the zeta and Gamma functions are asymmetric. We show their global minimum along the x-direction throughout the critical strip, their zeros, and the non-trivial zeros of the zeta function must occur at s=1/2+iy. If the zeros were not along the critical line, we show contradictions to the properties of the symmetric functional pair would arise. Thus, we prove rigorously the validity of Riemann’s conjecture.