Regularization for zeta functions with physical applications I

Abstract

We propose a regularization technique and apply it to the Euler product of zeta functions, mainly of the Riemann zeta function, to make unknown some clear. In this paper that is the first part of the trilogy, we try to demonstrate the Riemann hypotheses by this regularization technique and show conditions to realize them. In part two, we will focus on zeros of the Riemann zeta function and the nature of prime numbers in order to prepare ourselves for physical applications in the third part.