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

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.