2023Unpublished venueOpen access

Proof that the Real Part of All Non trivial Zeros of Riemann Zeta Functions is 1/2

Xiaohui Li

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Abstract

By analytically extending the Euler Zeta function, the Riemann Zeta function is obtained. The Riemann Zeta function has zero points, which are trivial and non trivial, respectively. By analyzing the internal structure of the Riemann Zeta function, it was found that the key to the value of 0 in the complex plane of the Riemann Zeta function is sin(sπ)=0, thus proving the validity of the Riemann hypothesis. That is, the real parts of all non trivial zeros of the Riemannian Zeta function are on the complex plane 1/2.

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By analytically extending the Euler Zeta function, the Riemann Zeta function is obtained. The Riemann Zeta function has zero points, which are trivial and non trivial, respectively. By analyzing the internal structure of the Riemann Zeta function, it was found that the key to the value of 0 in the complex plane of the Riemann Zeta function is sin(sπ)=0, thus proving the validity of the Riemann hypothesis. That is, the real parts of all non trivial zeros of the Riemannian Zeta function are on the complex plane 1/2.

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Available abstract

By analytically extending the Euler Zeta function, the Riemann Zeta function is obtained. The Riemann Zeta function has zero points, which are trivial and non trivial, respectively. By analyzing the internal structure of the Riemann Zeta function, it was found that the key to the value of 0 in the complex plane of the Riemann Zeta function is sin(sπ)=0, thus proving the validity of the Riemann hypothesis. That is, the real parts of all non trivial zeros of the Riemannian Zeta function are on the complex plane 1/2.

Key concepts: Riemann zeta function, Particular values of Riemann zeta function, Riemann hypothesis, Riemann Xi function, Arithmetic zeta function, Proof of the Euler product formula for the Riemann zeta function, Mathematics, Explicit formulae

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