Selected Theorems of the Riemann Zeta Function and Applications

One the contributions are that we have found details of auxiliary claims inside proofs of the Euler product formula of Riemann zeta function; the analytic continuation of the Riemann zeta function; the functional equation of the Riemann zeta function and the Prime Number Theorem which were given without proofs in the above papers and books. The second our contributions are that we succeeded to divide very long proofs into steps with informative explanations of the aims (purposes) of all steps.