About the Riemann Hypothesis

Jinhua Fei

doi:10.4236/jamp.2016.43061

Abstract

The Riemann hypothesis is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems. It is also one of the Clay Mathematics Institute’s Millennium Prize Problems. Some mathematicians consider it the most important unresolved problem in pure mathematics. Many mathematicians made a lot of efforts; they don’t have to prove the Riemann hypothesis. In this paper, I use the analytic methods to deny the Riemann Hypothesis; if there’s something wrong, please criticize and correct me.

Highlights

Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes Less than a Given Number”
Hypothesis is closely related to the well-known Prime Number Theorem
The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line”

Summary

Introduction

Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes Less than a Given Number”. It is one of the unsolved “super” problems of mathematics. Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line”. We use the analytical methods, and refute the Riemann Hypothesis. We will abbreviate the Riemann Hypothesis as RH

Some Theorems in the Classic Theory

Some Preparation Work