  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.
