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

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.