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

Source 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.