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Article

A Proof of Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

This version is not peer-reviewed.

Submitted:

02 August 2021

Posted:

05 August 2021

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Abstract
The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series. Thus, $\xi(s)=0$ corresponds to an algebraic equation with real coefficients and infinite degree. In addition, by $\xi(s)=\xi(1-s)$, another formally equivalent algebraic equation exists, i.e., $\xi(1-s)=0$. Then these two simultaneous algebraic equations share the common solution, thus a proof of Riemann Hypothesis (RH) can be obtained.
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Subject: 
Computer Science and Mathematics  -   Algebra and Number Theory
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