# A proof of Riemann Hypothesis

## TL;DR

This paper claims to prove the Riemann Hypothesis by constructing a special function related to the zeta function and analyzing its properties to show all nontrivial zeros lie on the critical line.

## Contribution

It introduces a new function and boundary value problem approach to prove all nontrivial zeros of the zeta function have real part 1/2, claiming to prove the Riemann Hypothesis.

## Key findings

- All nontrivial zeros of ta function have real part 1/2.
- The constructed function satisfies a boundary value problem at zeros.
- The proof concludes the Riemann Hypothesis is true.

## Abstract

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