The rightness of the Riemann Hypothesis

TL;DR

This paper argues that the Riemann Hypothesis is correct by showing that any zeros off the critical line lead to a contradiction, based on properties of certain functions related to the zeta function.

Contribution

It provides a proof that the zeros of the Riemann zeta function must lie on the critical line, supporting the Riemann Hypothesis.

Findings

Zeros off the critical line lead to contradictions.

Supports the validity of the Riemann Hypothesis.

Uses properties of functions related to the zeta function.

Abstract

The properties of several functions are employed to investigate the zeros of the Riemann zeta function $\zeta(a+bi)$ $(0<a<1, b\neq 0)$. If the zeros of the zeta function have not the form $\frac{1}{2}+ib$ where $i=\sqrt{-1}$, we derive a contradiction, illustrating that the Riemann Hypothesis is right.