Proving the Truth of the Riemann Hypothesis by Introducing the Generating Function for Prime Numbers

Abstract

The Riemann zeta function  plays a crucial role in number theory and its applications. The Riemann Hypothesis (RH) posits that zeros of  other than the trivial ones are located on the line defined by the equation Re(s) =1/2. This paper introduces proof of the Riemann Hypothesis. The proof employs a standard method, utilizing the eta function in place of the zeta function, under the assumption that the real part is greater than zero. The equation for the real and imaginary parts of the Riemann zeta function (eta function) is completely separated. Additionally, using a standard method and with the help of two functions ?(s) and ?(1-s), the real part of the root of the zeta function is obtained. To create a generator function for prime numbers in terms of b, one can solve the root of the zeta function where it equals one (i.e.,  and obtain a relationship between b’ and prime numbers.