The Regularization for the Zeta Functions with Physical Applications II

Abstract

We have proposed a regularization technique and applied it to the Eu ler product of the zeta functions in the part one. In this paper that is the second part of the trilogy, we aim the nature of the non-trivial zero for the Riemann zeta function which gives us another evidence to demonstrate the Riemann hypotheses by way of the approximate functional equation.Some other results on the critical line are p resented using the relations between the Euler product and the deformed summation representations in the critical strip. We also discuss a set of equations which yields the primes and the zeros of the zeta functions. In part three, we will focus on physical applicat ions using these outcomes.