A proof of Riemann Hypothesis

Abstract

Let $\hat{I}ž(t)$ be a function relating to the Riemann zeta function $\hat{I}\P (s)$ with $s=\frac{1}{2}+it$. In this paper, we construct a function $v$ containing $t$ and $\hat{I}ž(t)$, and prove that $v$ satisfies a nonadjoint boundary value problem to a nonsingular differential equation if $t$ is any nontrivial zero of $\hat{I}ž(t)$. Inspecting properties of $v$ and using known results of nontrivial zeros of $\hat{I}\P (s)$, we derive that nontrivial zeros of $\hat{I}\P (s)$ all have real part equal to $\frac{1}{2}$, which concludes that Riemann Hypothesis is true.

15Pages