The Proof of the Riemann Conjecture
Abstract:
In order to strictly prove the conjecture in Riemann's 1859 paper on the Number of prime Numbers Not Greater than x from a purely mathematical point of view, and strictly prove the correctness of Riemann's conjecture, this paper uses Euler's formula to prove that if the independent variables of ζ(s) function are conjugate, then the values of ζ(s) function are also conjugate, thus obtaining that the independent variables of ζ(s) function are also conjugate at zero. And using the conjugation of the zeros of the Riemann ζ(s) function and the zeros of ζ(s)=0 and the zeros of ζ(1-s)=0, s and 1-s must also be conjugated, The nontrivial zero of Riemann function ζ(s) must meet s= 1/( 2 )+ti(t ER and t≠0) and s= 1/ ( 2 )-ti(t E R and t≠0). And the symmetry of the zeros of Riemann ζ(s) function is the necessary condition that the non trivial zeros of Riemann ζ(s) function are located on the critical boundary. According to the symmetry property of the zeros of Riemann ζ (s) function s and the zeros of Riemann ζ(s) function 1-s, combined with the conjugated property of the zeros of Riemann ζ(s) function s and Riemann ζ(s) function 1-s, It is shown that the real part of the nontrivial zero of the ζ(s) function must only be equal to 1/( 2 ). And by Riemann set s=1/2+ti(t EC and t≠0) and auxiliary function ξ(s)=1/2s(s-1) EΓ(s/2)π E (- s/2) ζ(s)(s EC and s≠1), Get ∏ s/2(s-1)π^(-s/2)ζ(s)= ξ(t) =0, combining the nontrivial ze ros of Riemann function ζ(s) must meet s =1/( 2 )+ti (t E R and t≠0) and s =1/( 2 )-ti (t E R and t≠0), Thus it is proved equivalently that the zeros of the Riemann ξ(t) function must all be non-zero real numbers, and the Riemannian con jecture is completely correct.
