The Riemann hypothesis - an elementary analytic approach based on complex Laplace transform

TL;DR

This paper presents an elementary analytic proof of the Riemann hypothesis using complex Laplace transform techniques and double integral representations of the Green function.

Contribution

It introduces a novel elementary approach to the Riemann hypothesis based on complex Laplace transforms and integral representations.

Findings

Provides an elementary proof of the Riemann hypothesis

Utilizes double real and complex Laplace integral representations

Highlights the role of Green function in the proof

Abstract

An elementary analytic proof of the famous Riemann hypothesis is given. The main "accent" of the proof is a both using of the 2-dimensional double real and complex Laplace integral representations of the Green function $\mid z \mid^{-2}$.